BAGHDAD — Secretary of State Rice said today that America, Iraq, and Turkey have a “common interest” in stopping Kurdish rebels in northern Iraq, but cautioned against taking any action that could destabilize the region.

Ms. Rice’s comments came two days after Turkey conducted airstrikes against rebels from the Kurdish Workers’ Party, or PKK, in northern Iraq. As many as 50 fighter jets were involved in the attack, the biggest against the PKK in years. The planes attacked several villages, killing one woman, Iraqi officials said.

The Turkish army also sent soldiers about 1.5 miles into northern Iraq in an overnight operation today, Kurdish officials said. A Turkish official said the troops seeking Kurdish rebels were still in Iraq by midmorning.

Ms. Rice made it clear that America supports efforts to quash any rebel movement, but she said it was a “Turkish decision” to act.

And she suggested that Iraqi, Turkish, and American authorities should try to work together against the rebels.

“This is a circumstance in which … we need an overall comprehensive approach to this problem,” Ms. Rice said. “No one should do anything that threatens to destabilize the north.”

“This was a Turkish decision,” Ms. Rice said of the Sunday airstrike. “And we have made clear to the Turkish government that we continue to be concerned about anything that could lead to civilian casualties or anything that could destabilize the North.”

Iraq’s foreign minister, Hoshyar Zebari, said at their joint news conference that America, Iraq, and Turkey share a goal of making sure there is no “PKK terrorist activity,” including what have been cross-border attacks against the Turks from Iraqi territory.

Mr. Zebari said that Iraq understands what he said were Turkey’s “legitimate concerns” about the rebels, who want their own Kurdish state, although the Baghdad government had complained that Ankara didn’t notify Iraq of the airstrikes in advance. But Mr. Zebari said it’s better if Iraq, Turkey, and America work jointly to come up with a plan to quash the Kurdish rebels.

“We believe any unilateral actions to destabilize the situation will harm Iraqi interests and Turkey’s interests,” Mr. Zebari said.

Ms. Rice began an her unannounced visit with a trip to Kirkuk in the oil-rich Kurdish region up north, where the American administration emphasized what it sees as new signs of cooperation and progress. She met with members of a civilian-military reconstruction unit based in the mixed city and with about two-dozen provincial politicians of all stripes.

“It is an important province for the future of Iraq, for a democratic Iraq, an Iraq that can be for all people,” she said at the start of the meeting with the provincial leaders.

Sunni Arabs ended a yearlong political boycott earlier this month in Kirkuk — the hub of Iraq’s northern oil fields — under a deal that sets aside government posts for Arabs. It was the biggest step yet toward unity ahead of a referendum on the area’s future.

“We see a logjam breaking here,” Ms. Rice’s senior adviser on Iraq, David Satterfield, said

Ms. Rice’s message to Iraqi leaders sounded familiar: Stop squabbling. But Mr. Satterfield said there is a twist.

“She’s saying, ‘look, see what’s been done as a result of your efforts, our efforts, on security, on economics. You guys have gotta catch up,” Mr. Satterfield said.

Kirkuk is an especially coveted city for both the Shiite-dominated Iraqi government in Baghdad and the Kurdish one in Irbil.

Kurds want to incorporate it into their self-rule area, but the idea has met stiff resistance from Arabs.

Much of Iraq’s vast oil wealth lies under the ground in the region, as well as in the Shiite-controlled south. Kurds refer to Kirkuk as the “Kurdish Jerusalem,” and control of the area’s oil resources and its cultural attachment to Kurdistan have been hotly contested.

Ms. Rice met in Baghdad with the U.N. new special envoy to Iraq, whose first task will be managing competing interests leading up the Kirkuk vote. America has long sought such a U.N. role, but the world body moved slowly after the assassination of its top envoy in Baghdad in 2003.