WASHINGTON — In the aftermath of an ambush yesterday by Kurdish separatists against Turkish soldiers in Daglica, America’s diplomats and generals are quietly pressing Iraq’s Kurdish regional government to use its Peshmerga militia to root out the Kurdish rebels’ strongholds on the Iraqi side of the Turkish border.

A State Department spokesman, Sean McCormack, issued a statement condemning the attacks in Daglica in the Hakkâri province of Turkey, calling the separatist Kurdistan Workers Party, or PKK, a “terrorist organization” that “has wrought a trail of bloodshed that serves only to perpetuate suffering.” The attacks killed at least a dozen Turkish soldiers; the PKK also suffered an estimated 32 casualties.

America is calling “upon Iraqi and Kurdish regional government authorities to take immediate steps to halt PKK operations from Iraqi territory,” Mr. McCormack said.

An Iraqi diplomat and an American military officer, who both requested anonymity, confirmed yesterday that the American ambassador to Iraq, Ryan Crocker, last week began quietly inquiries into the prospect of a Peshmerga offensive inside the Kandil mountain range against what is believed to be the headquarters of the PKK. After yesterday’s attacks and subsequent clashes, the likelihood of a Turkish offensive into northern Iraq increased considerably. The Turkish parliament overwhelmingly approved incursions into Iraq against the PKK on Wednesday, and the civilian and military leadership met just after midnight in Turkey to discuss possible military steps.

The Bush administration, meanwhile, has been negotiating with the Turks for more time, wary that any Turkish incursion into northern Iraq not only could destabilize the most stable region in Iraq but also could set a precedent for military incursions by the country’s other neighbors.

Defense Secretary Gates is predicting that no Turkish military action is imminent, the Associated Press reported. But the signals were mixed yesterday from Ankara. On the government’s official Web site, a statement from President Gül said Turkey would “pay any price” to defeat the PKK wave of terror.

Asked about the prospect of the Kurdistan regional government launching an offensive into the PKK strongholds along the border with Turkey, its Washington representative, Qubad Talabani, said it was not likely.

“We don’t think there is a military solution. There has never been a military solution. We have been always willing to entertain nonmilitary solutions for this,” Mr. Talabani, whose father is Iraq’s president, told The New York Sun.

The author of “Blood and Belief: The PKK and the Kurdish Fight for Independence,” Aliza Marcus, said that while Iraqi Kurds have attacked the PKK in the past, they would not be expected to agree to do so today.

“In 1992, they actively fought on Turkey’s behalf against the PKK,” she said. “They don’t want to be seen as fighting on Turkey’s behalf.”

Ms. Marcus added that the PKK has moderated its initial hostile stance toward the Iraqi Kurdish parties and that prior military skirmishes between PKK and the Patriotic Union of Kurdistan, one-half of the ruling coalition in Iraqi Kurdistan today, led to a military stalemate and failed to drive the PKK leaders from their mountain bases.

“There is almost no chance the Iraqi Kurds are going to attack the PKK,” she said. “Not only have they said that, but in fact they have no real strength to do it right now. They are not going to send their fighters into the mountains for a battle they know they will lose.”

The director of the Turkey program at the Brookings Institution, Omer Taspinar, said yesterday’s attacks increased the likelihood of a Turkish military response.

“I think it is a little too late in the game for either” the president of the Kurdistan regional government of Iraq, Massoud Barzani, “and Talabani to unleash Peshmerga to the region,” he said. “Turks would like to see results at this point.”

Mr. Taspinar also said he expected that the initial Turkish response would not be a military one. “The first step is to close the border, then cut the electricity,” he said. “That is what I am hearing. It would start incrementally. They have been asking the Kurdish government to take care of this for two years now. They want them to hand over PKK leaders believed to be in Suleimaniyah and Irbil. Before the Turks engage in a military operation, the Kurds could hand over leaders the Turks believe the regional government harbors.”