Washington ? Hours before his trip to the Middle East, Secretary of State Colin Powell said Sunday he believes Israel “understands clearly” President Bush’s demand for an end to the offensive in Palestinian territories.

Despite Bush’s call for a withdrawal “without delay,” Israel pressed ahead Sunday with its 10-day campaign to apprehend militants throughout the West Bank.

Israeli Prime Minister Ariel Sharon, who spoke to Bush on Saturday and Powell on Sunday, pledged to try to “expedite” the military operation, according to an Israeli statement, but did not announce a timetable for a withdrawal.

“The president doesn’t give orders to a sovereign prime minister of another country,” Powell said. “But as one of Israel’s best friends and most supportive friends, I think Prime Minister Sharon has taken very much to heart and he understands clearly the message the president gave to him.”

Powell said Bush “is expecting without delay, meaning now. And so we’ll see how the prime minister responds in the very near future.”

But he also said the two leaders “did not talk about a specific end point.” Israel has had a massive buildup, Powell said. “It isn’t going to be over when they do start to withdraw. It’s not going to be over in a day. It took a while to do it, and they are still conducting operations,” he said on “Fox News Sunday.”

Powell said the United States understood the need for Israel to defend itself against suicide bombers. But the continuing offensive is producing signs of possible long-term damage to peace prospects in the region, the secretary of state said.

“We may well be radicalizing a new generation, many more terrorists waiting to act once this incursion is over.”

While the bombings have stopped in recent days and Sharon told Powell on Sunday that Israel has thwarted another potential attack, Powell said that a political solution is the only way to resolve the Israeli-Palestinian conflict.

“We have to realize that, sooner or later, Israel will withdraw its forces, and those same pressures will be there, that same frustration will be there, that same anger will be there,” he said.

“And perhaps it’ll be even greater and will give rise to this kind of activity again – unless the Palestinians see hope, unless the Palestinians see Israel, the United States, the Palestinian leaders, the Arab leaders, the international community all coming together to support a cease-fire which rapidly leads to negotiations that will create a political solution.”

Powell was to leave Sunday night, with stops in the Middle East and Europe. He said he would meet with Sharon, possibly as early as Thursday. On NBC’s “Meet the Press,” he said he would meet with Palestinian leader Yasser Arafat “if circumstances permit.”

Arafat remains confined to his compound in Ramallah, surrounded by Israeli troops.

U.S. officials outlined those circumstances as Israel allowing Powell entry into Arafat’s offices, as they did last week for U.S. envoy Anthony Zinni; security steps to ensure Powell’s safety; and an expectation that a meeting would be worthwhile.

On ABC’s “This Week,” national security adviser Condoleezza Rice said Bush believes “the situation in the Middle East is now at a tipping point.”

“He has said to our good friend Israel that it is time to begin withdrawal from the occupied areas, the areas they’ve recently occupied, and it is time to reverse and to change the dynamics of the situation,” she said.

In a blunt telephone call Saturday from his ranch in Crawford, Texas, Bush told Sharon that Israel needed to make progress quickly if the American peace effort was to succeed, aides said.

Bush expressed “deep concerns” for the attacks into Palestinian cities and called on Sharon to pull his troops back, the officials said. They described the 20-minute conversation as tense.

“Israel should halt incursions in the Palestinian-controlled areas and begin to withdraw without delay from those cities it has recently occupied,” Bush said during a news conference with British Prime Minister Tony Blair.

Bush also demanded the Palestinians immediately call a cease-fire. Powell echoed the point Sunday.

“Until the violence goes down at least to a level where you can see that both sides are acting in a responsible way and trying to cooperate in a cease-fire, you’re not going to get to a peace agreement,” he said on NBC.