WASHINGTON — America, NATO, and Britain are all supporting Turkish strikes and a brief incursion into northern Iraq to root out positions alleged to belong to the Kurdistan Workers’ Party.

The support for the Turkish strikes yesterday represents a shift for America and Europe, which have cautioned the Turks against a serious military incursion. But tensions on the border between northern Iraq and Turkey boiled over when the Kurdish separatist group, known as the PKK, aired a video of Turkish soldiers it abducted in raids earlier this week.

“Our understanding is that Turkish forces carried out limited incursions into Iraqi territory in pursuit of PKK targets,” a State Department spokesman, David Foley, said.

He added: “We support the Turkish government in their defense of Turkey against terrorism. We urge restraint against actions that would destabilize the region.”

Also yesterday, Secretary of State Rice told the House Foreign Affairs Committee that she hoped a meeting scheduled for today in Ankara between the Iraqis and the Turks would ease border tensions. Meanwhile, Defense Secretary Gates said America and Turkey needed better intelligence before committing to airstrikes in the Qandil mountains, where the PKK leadership is believed to be hiding out.

American and Iraqi military officials told The New York Sun that Turkey conducted the airstrikes into Kurdish territory with American-made F–16 jets and that a small group of commandos crossed over the border in the Qandils. The border there is not marked well, and the incursion was no more than a few miles, an Iraqi official said.

Much is riding on today’s meeting at Turkey’s capital. The Turks believe that the Kurdistan regional government in northern Iraq knows the locations of senior PKK leaders and that on occasion those leaders have even ventured into the regional capital of Irbil, the director of the Turkish research program at the Washington Institute for Near East Policy, Soner Cagaptay, said.

“I think the first thing the Turks are looking for is that the PKK is not violating the Turkish-Iraqi border; as long as the PKK is crossing the border and killing people, all this rhetoric looks superficial,” Mr. Cagaptay said. “The elimination of the PKK’s top leadership, that is what the Turkish government is looking for right now.”

The Turkish foreign minister, Ali Babacan, said yesterday that if Kurdish and Iraqi leaders were not prepared to present a plan of action to eliminate the PKK in northern Iraq, today’s meeting would fail.

President Talabani of Iraq, who is also the head of the Patriotic Union of Kurdistan, denied reports that Kurds in Iraq would hand over PKK leaders, insisting that even the Kurdish leaders do not know their locations.

Nonetheless, Iraq made two key concessions against the PKK, which America and Turkey have said is a terrorist organization. Prime Minister al-Maliki announced that Iraq would close the PKK offices in the country. In addition, the president of the Kurdistan regional government, Massoud Barzani, son of the most storied Kurdish leader of the 20th century, Mustafa Barzani, called on Turkish Kurds to stop their armed rebellion.

The author of “God and Gold: Britain, America, and the Making of the Modern World,” Walter Russell Mead, said he did not think the Turkish moves into northern Iraq would risk setting a precedent for armed intervention from Iran or Syria. “As a pragmatic matter, the fact that Turkey received a statement of support from NATO, if those countries tried it, they would find themselves isolated,” Mr. Mead, a senior fellow at the Council on Foreign Relations, said.

Still, he said the developments posed their own risks. “The risk with any armed conflict is that it can spread,” he said. “They may find the airstrikes don’t make the terror raids stop, and they decide to go in by land and step up the airstrikes. The security situation could deteriorate and could have a wider impact on the politics of Iraq, where the Kurds play an important role.”

An American military official who requested anonymity said he doubted that the tensions would flare into a broader Turkish-Kurdish war. “The Turks, for their own domestic political reasons and for their prestige, have to send a message: ‘You can’t just abduct soldiers with impunity,'” the official said. “But at the same time, the reason the PKK grabbed the people was to instigate a border incursion because it will save them politically in Turkey. The Kurdish government in Iraq does not want that, and neither do the Turks.”