By STEVEN R. WEISMAN - Published: April 26, 2006

ANKARA, Turkey, April 25 - Secretary of State Condoleezza Rice assured Turkish leaders on Tuesday that the United States would step up efforts to stop Kurdish insurgents in Iraq from infiltrating into Turkey, but she cautioned the government not to send troops to Iraq to do the job.

The Turkish foreign minister, Abdullah Gul, said there had been a surge in infiltration in recent weeks.

Ms. Rice, addressing what has become a new irritant in relations with Turkey, acknowledged that the problem had been allowed to grow. The Turkish news media has been filled with reports of thousands of Turkish troops massing on the border with Iraq, and there has been speculation that Turkey might intervene in Iraq.

"Of course we want anything that we do to contribute to stability in Iraq, not to threaten that stability or to make a difficult situation worse," Ms. Rice said, referring to Turkish troops. "That is why a cooperative approach on this problem -  cooperation between Iraq and Turkey and the coalition forces - is very important."

Mr. Gul spoke of the Kurdish rebel situation in blunt terms, saying that the Kurdish Workers Party had turned Iraq into "a training ground" and that "Turkey will take her own precautions" to deal with the problem.

He said, however, that Turkey had "no claim on anybody's soil or any neighborly country's soil."

Ms. Rice, on a tour through the region, started in the morning with meetings in Athens, where several thousand anti-American protesters thronged the streets downtown. A few dozen protesters threw gasoline bombs. Police officers in full riot gear used tear gas to disperse demonstrators trying to march on the United States Embassy.

In Greece, Ms. Rice sought to win approval of Security Council action to raise pressure on Iran to suspend its uranium enrichment, which is believed in the West to be a cover for a nuclear weapons program. Iran says it is for civilian nuclear power.

Greece is currently a member of the Security Council, and the Greek foreign minister, Dora Bakoyannis, expressed solidarity with the American objective of stopping Iran's suspected nuclear weapons program, but hinted that she did not think the time was right for Security Council action.

"We are in the middle of a diplomatic effort, a diplomatic effort which still has some tools to use in order to become effective," she said.

Outside the meeting, the demonstrators were protesting the possibility of American military strikes against Iran, and inside a Greek journalist asked Ms. Rice whether the United States would seek to use military bases or facilities in Greece for military intervention against Iran.

The question and the demonstrators suggested that the United States has to contend in Europe with not only the fallout from the Iraq war but also an outcry against using force in Iran.

"Let me go right to the crux of the question," Ms. Rice said. "The United States of America understands and believes that Iran is not Iraq."

In Turkey, Ms. Rice said she appreciated its support for the recent efforts to form a nationally unified government in Iraq. Turkey is fearful of a breakup of Iraq because it is concerned that the Kurdish population in the north could help foment a Kurdish rebellion in Turkey.

Ms. Rice said the United States would share intelligence with Turkey in an effort to help prevent the movement of Kurds.

"We believe that it is important that we make a joint effort through information-sharing and other means to prevent any vacuum from being used as a way to inflict harm here in Turkey," she said, referring to a lack of American and Iraqi forces that may have contributed to the problem.