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“What matters is not necessarily the formal severity of the crime but the potential harm in the public’s faith in the government and whether the person can continue to project integrity,” he said. “This is the foreign minister of Israel. … He is the face that represents us, and the actions attributed to him become part of the image of the state of Israel.”

Three opposition leaders — Shelly Yachimovich of Labor, former Foreign Minister Tzipi Livni of the new “Movement” Party and Yair Lapid of the Yesh Atid Party — all called for Mr. Lieberman‘s dismissal.

Court rulings in other, more serious criminal cases against Cabinet officials forced them to resign. Facing the prospect of an indictment, former Prime Minister Ehud Olmert announced his decision to step down in 2008 before formal corruption charges were filed against him. Olmert this year was cleared of most charges but convicted of breach of trust.

The blunt-talking Mr. Lieberman has amassed power with support from immigrants from the Soviet Union and other Israelis drawn to his broadsides against Israeli Arabs and dovish groups, as well as the Palestinians and Western Europe.

Mr. Lieberman, who once worked as a bar bouncer, immigrated to Israel in 1978 from Moldova in the former Soviet Union.

Speaking in a Russian-accented monotone, he became a national figure in 1996 as a top aide to Mr. Netanyahu during his previous term as prime minister. He later quit Mr. Netanyahu’s Likud party and was elected to parliament in 1999 as head of Yisrael Beitenu (Israel Our Home), a secular hawkish party he established to represent the more than 1 million immigrants from the former Soviet Union.

His party has gained strength since then. It was the third largest in 2009 elections, drawing many votes from native Israelis as well as his traditional base.

Mr. Lieberman is known for inflammatory rhetoric that has at times agitated his partners in government. He has called for executing Israeli Arab lawmakers who met with leaders of the Palestinian militant group Hamas. As an opposition lawmaker in 2008, he said Egypt’s then-President Hosni Mubarak “can go to hell.”

More recently, Mr. Lieberman pushed a series of legislative proposals that critics said were anti-Arab, including a failed attempt to require Israelis to sign a loyalty oath or have their citizenship revoked, and calls to redraw Israel’s border to place Arab towns under Palestinian jurisdiction.

He embarrassed Mr. Netanyahu in the past by expressing contrasting views to that of the government, including skepticism over the chances of reaching peace with the Palestinians.

Mr. Lieberman has called Palestinian President Mahmoud Abbas an “obstacle to peace” and urged his removal so that peace talks that collapsed in 2008 could be revived.

Earlier this week, he lashed out at the international community, saying many world leaders would sacrifice Israel to radical Islam just as Europe appeased the Nazis before World War II.