Several hundred Turkish troops crossed into northern Iraq on Tuesday and engaged in clashes with Kurdish guerrillas, Turkish military officials said, as U.S. Secretary of State Condoleezza Rice made an unannounced visit to Iraq to tout security gains.

Rice encountered frustration from some Iraqi Kurdish leaders upset that the U.S. is allowing Turkish forces to operate inside Iraq. Turkey is combating the Kurdistan Workers’ Party, or PKK, which says it is fighting for greater Kurdish autonomy in Turkey and uses northern Iraq as a base.

Massoud Barzani, president of the Kurdistan Regional Government, a semiautonomous body that administers three predominately Kurdish provinces in northern Iraq, refused to attend a meeting with Rice on Tuesday.

“The president justified his rejection in that the Iraqi sky is controlled by U.S. forces, and these forces allowed Turkish aircraft to breach Iraqi borders to bomb Kurdish villages and that caused causalities among the Kurdish citizens,” said Fouad Hussein, an aide to Barzani, referring to Turkish airstrikes Sunday.

After a stop in the northern Iraqi city of Kirkuk, about 120 miles south of where Turkish troops launched their incursion, Rice told reporters in Baghdad that the United States, Turkey and Iraq have a common interest in “stopping the activities of the PKK” but cautioned that “no one should do anything that threatens to destabilize the north.” The group is accused of killing more than 50 Turkish security personnel and civilians in recent months in cross-border raids.

On Tuesday in Washington, defense and diplomatic officials said that U.S. military commanders in Iraq didn’t know Turkey was sending warplanes to bomb in northern Iraq until the planes had already crossed the border.

Americans have been providing Turkey with intelligence to go after Kurdish rebels in northern Iraq. And a “coordination center” has been set up in Ankara so Turks, Iraqis and Americans can share information, two officials said Tuesday.

But defense and diplomatic officials in Washington and Baghdad told The Associated Press that U.S. commanders in Iraq knew nothing about Sunday’s attack until it was already under way.

They spoke on condition of anonymity because they were not authorized to speak on the record.

Their comments follow complaints by Iraqi leaders Monday that Turkey hadn’t coordinated with Baghdad before sending bombers to strike targets of the Kurdistan Workers’ Party, or PKK.

It was left to the Americans to inform Iraqi government officials of Sunday’s incursion, one U.S. official said.

No problem occurred with a conflict in the air space, but might have as both military and commercial flights go through northern Iraq, the officials said.

U.S. diplomatic officials also expressed irritation that the Turks had not provided them or the Iraqis with advance notice of the operation and said they had made their displeasure clear.