Egyptian President Hosni Mubarak's offer to host a summit between Israeli and Palestinian leaders has fallen on deaf ears in Israel.

Mubarak proposed to Israeli Prime Minister Ariel Sharon last week that he meet with Palestinian leader Yasser Arafat.

The suggestion was rebuffed by the Israelis, who said there was nothing to be gained from such a meeting.

"We've had countless summits with Arafat and we think it's an illusion to think anything would change now because of another one," an Israeli official told Fox News.

But with Israel cold to the overture, Secretary of State Colin Powell also rejected the idea, adding that the United States is grateful for Mubarak's interest.

"I appreciate the continuing interest (Mubarak) has shown in trying to find a solution," Powell said Monday. "His idea is an interesting one, but of course it's up to the two individuals, Mr. Arafat and Mr. Sharon, to decide which forums they would participate in."

The United States has looked to Egypt and a handful of Arab countries for peacemaking support for three decades.

The Egyptian president's help is especially vital as the current intifada grows more violent, and many Arab governments, and most Arabs in private, regard the Bush administration as hopelessly tilted in Israel's favor. In fact, the U.S. response may be due to the fact that Sharon is unenthusiastic about such a summit.

Fighting between Israelis and Palestinians escalated sharply this past week, the latest tit-for-tat cycle of 17 months of violence that has left over 1,000 people dead, most of them Palestinians.

Israeli forces attacked Palestinian Authority headquarters in Bethlehem and Ramallah Monday, killing 16 Palestinians. The assault was in retaliation for a sniper attack that killed 10 Israelis at a West Bank checkpoint Sunday.

The sniper attack followed a suicide bombing outside a synagogue Saturday evening in which several Israeli children were killed.

The targeting of Arafat's headquarters in Bethlehem was meant to send the message that, as Israeli officials put it, "if you behave like a statesman, we'll treat you like a statesman — if you behave like a terrorist, we'll treat you like a terrorist."

Mubarak's offer followed the floating of Saudi Crown Prince Abdullah's proposal for most Arab countries to recognize the Jewish state in exchange for Israeli withdrawal from the territories it captured during the 1967 Six-Day War.

Abdullah had been formally withholding his peace initiative, which was applauded in the Israeli press but not warmly received by the Israeli coalition government, until the Israeli army lifted restrictions on Arafat's movements within the West Bank and Gaza Strip.

Arab governments have questioned whether Arafat can be expected to take strong measures against terror if his movements are restricted. Abdullah is expected to make his proposal official during an Arab League meeting later this month.

Mubarak, in town to meet with President Bush and other administration officials, also urged the United States to use caution before attacking Iraq.

The Bush administration considers Iraq, a member of President Bush's "axis of evil," to be a supporter of terrorism. American concern over Saddam Hussein's pursuit of weapons of mass destruction has placed it high on the U.S. list of potential targets.

Mubarak has been generally supportive of the U.S.-led war against terrorism, and has warned that terrorists may still have sleeper cells in the United States waiting to strike again.

Mubarak met with Secretary of State Colin Powell Tuesday for 45 minutes but made no statements. He is to meet with Bush Tuesday and has scheduled meetings with Vice President Dick Cheney, Defense Secretary Donald Rumsfeld, National Security Adviser Condoleezza Rice, and CIA Director George Tenet.

Fox News' Teri Schultz and the Associated Press contributed to this report.