The addition of Mr. Lieberman to the government — which has been widely reported in the Israeli news media but not officially announced — would further cement the rightist nature of Mr. Netanyahu’s coalition.

Mr. Yaalon, 65, is at the center-right of the political spectrum, but has served as a bulwark against the most extreme populist sentiments criticizing the military and the Likud coalition, by Mr. Lieberman and others. He said he planned to return someday to political life, including a run for state leadership.

“I fought with all my might against phenomena of extremism, violence and racism in Israeli society that threaten its fortitude,” he said, adding that these forces “ are trickling into” the military.

The contrast in military credentials between Mr. Yaalon and Mr. Lieberman could hardly be more pronounced. Mr. Yaalon, a former chief of staff and career general, led commando units and took part in daring operations. Mr. Lieberman left the military at the rank of corporal. He is known for hard-right positions like demanding the death penalty for Palestinians convicted of terrorism and the toppling of Hamas, the militant group that rules Gaza.

Mr. Yaalon came under fire for quickly condemning the actions of an Israeli soldier who shot and killed a wounded Palestinian assailant in the West Bank city of Hebron. Many Israelis viewed Mr. Yaalon’s immediate statement that the soldier should be brought to justice because he had violated military code as prejudging the case and troops at a time when they face violent attacks by Palestinians.

Mr. Netanyahu at first took a similar stand, but he later called the soldier’s father, a move that was seen as offering support.

“With great sorrow, senior politicians in the country have chosen incitement and divisiveness of the Israeli society instead of unifying and connecting,” Mr. Yaalon said. “It is unacceptable to me that we be divided because of cynicism or craving for control, and I expressed more than once my opinion on the matter — from a position of sincere worry for the future of Israeli society and future generations.”