ISTANBUL, Turkey – Turkey warned Thursday that U.S. objections will not stop its troops from crossing into Iraq to pursue Kurdish separatists, while a steady stream of U.S.-made Turkish fighter jets roared across the skies along the border.

High-level Iraqi officials arrived in Turkey as part of frantic efforts to persuade the government not to order an attack on Kurdish guerrilla bases in northern Iraq, and the U.S. ambassador to Iraq sent American diplomats to join the delegation.

Turkey’s leaders have been demanding that U.S. and Iraqi authorities stop Kurd rebels from staging attacks across the frontier, threatening to send in a large offensive if nothing is done soon.

Turkey still seems willing to refrain from a big attack until at least early next month, when it is scheduled to host foreign ministers to discuss Iraq. Prime Minister Recep Tayyip Erdogan is expected to go to Washington afterward for talks with President Bush.

Turkish artillery has been periodically firing across the border, and Turkish television showed video of smoke rising from three villages in northern Iraq that were purportedly hit by shells Thursday.

Dogan news agency, which provided the footage, said there were no casualties because villagers had fled their homes. It did not cite a source. The agency identified one of the villages as Hezil, three miles from the border of Turkey’s Hakkari province.

The army, meanwhile, reported a clash with rebels earlier in the week. It said a “group of terrorists” was spotted preparing an attack near a military outpost in Semdinli province close to Iraq on Tuesday and troops opened fire with tank cannon, artillery and other heavy weapons.

The report on the military’s Web site also increased the official number for rebels killed since Sunday to at least 64.

U.S. officials are urging Turkey not to launch an incursion that could destabilize Iraq’s autonomous Kurdish north, the country’s most stable region.

But Erdogan said the U.S. desire to protect the north would not hinder Turkey’s fight against PKK guerrillas. The rebels use mountain bases in Iraq to rest, train and get supplies in relative safety before returning to Turkey to attack government forces.

The Bush administration “might wish that we do not carry out a cross-border offensive, but we make the decision on what we have to do,” Erdogan said.