The military leadership is concerned that anger over the government’s plan, with some pilots saying they will skip some training sessions and operations, could diminish military capabilities.

A plan by Prime Minister Benjamin Netanyahu to severely curtail the powers of Israel’s Supreme Court has prompted weeks of demonstrations, rattled the country’s technology sector and raised fears of political violence.

Now, protests are emerging even within the nation’s military.

Hundreds of soldiers in the military reserves either have signed letters expressing a reluctance to participate in nonessential duty or have already pulled out of training missions, officials said. The affected units include the 8200 division that deals with signal and cyberintelligence and whose graduates have helped drive the country’s tech industry, as well as elite combat units.

The military leadership fears that growing anger within the ranks over the government’s plans will affect the operational readiness of Israel’s armed forces, according to senior military officials.

It is most concerned about unrest within the Air Force, with reserve duty pilots increasingly upset over the government plans, the officials said. They also fear that they may be asked to engage in illegal operations, and that restraints on Israel’s judiciary may strengthen foreign calls to prosecute them in the International Criminal Court, the officials said. Reserve duty pilots often lead Israel’s regular airstrikes on Syria and the Gaza Strip, and would be involved in any major Israeli attack on nuclear facilities in Iran.

The unrest within the military is the latest flare-up of opposition to the government’s plans to overhaul the judiciary after protests brought hundreds of thousands of Israelis to the streets of cities like Tel Aviv. Prominent American Jews have also criticized the plans, and on Sunday, Michael Bloomberg, the former New York mayor, wrote in a New York Times guest essay that Mr. Netanyahu was “courting disaster.”

But for many Israelis, anger within the military is perhaps the most worrying and significant reaction to the plans, which would increase government control over how judges are chosen, limit the Supreme Court’s ability to strike down new legislation and make it easier for Parliament to overrule the court.

Nearly 50 squadron leaders representing hundreds of reserve pilots met on Friday with the head of the Israeli Air Force to express their misgivings about the government’s judicial overhaul efforts, according to five Israeli military officials who either attended the meeting or were briefed on it and who insisted on anonymity because they were not authorized to speak publicly. The pilot corps is overwhelmingly staffed by reservists who usually report for duty three or four times a month.

Thirty-seven pilots from a key F-15 fighter jet squadron later wrote to the Air Force chief to say they would pull out of training for part of this week, while stressing that they remained available for combat missions, according to three officials briefed on the letter.

Many Israelis believe the government’s plan to overhaul the judiciary will undermine the country’s democracy. That view is shared by many military officers, a number of whom have participated in regular protests, even as an analysis of polling data from November’s general election suggested that the governing coalition also received strong support from rank-and-file soldiers.

To the government’s supporters, the judicial changes it is pushing through Parliament are an essential means of giving a majority of elected lawmakers primacy over unelected judges. But to critics, the overhaul would remove one of the few checks on government overreach, in a country lacking a formal Constitution, threatening Israel’s minority rights.

Both sides have accused each other of attempting a coup, and a recent poll suggested that more than a third of Israelis fear civil war could break out because of the crisis. Israelis have attended mass rallies every week against the proposals since the start of the year, in one of the longest and biggest waves of protests in Israeli history.

These tensions are roiling the military, which was previously perceived as a social leveler that unified otherwise fragmented parts of society and which remains essential to the security of a country that is locked in several low-intensity conflicts, including with Iran.

The meeting on Friday between the nearly 50 officers from the reserve pilot corps and the Air Force commander, Maj. Gen. Tomer Bar, was held at Air Force headquarters, and it was tense and emotional, participants said.

According to several military officials, the reservists’ concerns included worries about the judicial overhaul itself, as well as the fear that the government, which is led in part by far-right political leaders, might order them to enact something they deemed illegal.

Last week, a far-right minister in the Defense Ministry, Bezalel Smotrich, who also doubles as the finance minister, called for the state to “wipe out” a Palestinian town at the center of recent violence in the occupied West Bank. One of the participants at the meeting asked how a pilot could know with confidence that when given the coordinates to bomb a certain target, he would not be serving such a goal, according to three officials.

Because the overhaul would undermine judicial independence in Israel, it might bolster the argument that the Israeli court system is not fit to adjudicate on alleged crimes committed by Israelis, according to Roy Schondorf, a recently retired deputy attorney general for international legal affairs.

In turn, that might heighten pressure on prosecutors at the International Criminal Court in The Hague to charge Israeli officers, according to Mr. Schondorf, who oversaw efforts to protect Israeli officers from international prosecution.

While no formal threats to avoid reserve duty were made at the meeting itself, all but three of the 40 members of Squadron 69, a key strike force that flies F-15 fighter jets, later wrote to General Bar to withdraw from training for part of this week, but remain available for combat missions.

In a joint letter to Mr. Netanyahu and Defense Minister Yoav Gallant on Monday, all 10 surviving former Air Force chiefs expressed “great concern” about the “processes happening in the state of Israel and in the Air Force.”

The letter added, “We are fearful for the consequences of these processes and the grave and palpable threat that can be perceived to the state of Israel.”

The government has largely dismissed the reservists’ concerns and warnings as the tantrums of a privileged elite fearful of losing its dominant role in society.

The wavering reservists are “not patriots,” Galit Distel Atbaryan, the minister of information, said in a social media post on Sunday night. “Not the salt of the earth. Not Zionists. Not the best of our guys. Not wonderful people. Not the people of Israel.”

On Monday evening, Mr. Netanyahu, who served as an officer in a commando unit, said in a speech that the reservists’ actions “threaten the foundation of our existence.”

“There is room for protest; there is no room for rejection” of military service, Mr. Netanyahu said, standing next to the far-right national security minister, Itamar Ben-Gvir, who was prevented from serving in the Army during the 1990s because of concerns over his extremist views.

But some government members have appeared more conciliatory. “The situation requires that we talk, and quickly,” Mr. Gallant, the defense minister, said in a video statement.

There is also debate among reservists themselves about whether to bring politics into military service.

As reports of reservists’ discontent spread over the weekend, a reserve general in the Air Force, Ori Seiffert, wrote an open letter to fellow reservists, asking that they continue to serve as pilots despite opposing the judicial overhaul.

“Like many of us, I am also very disturbed and afraid of the direction” of the government, General Seiffert wrote in the letter, which was obtained by The Times. But, he added, “We must maintain the power of the Air Force and the power of the Israel Defense Forces.”

“To my reservist brothers, I say, Protest and serve, serve and protest,” General Seiffert added.

Reservists who have already chosen to limit their volunteer duty said the decision had been extremely difficult. A reserve colonel in Unit 8200 — one of more than 500 reservists in the cyberdivision who signed a letter criticizing the overhaul — said that the decision had kept him up at night, and that he would swiftly return to service if war broke out.

“If we get into a situation where an offensive attack occurred against Israel,” said the 47-year-old colonel, who declined to be identified for fear of security threats from Israel’s foreign enemies, “all of us would be there to protect the citizens of Israel.”