A Kurdish faction allied with President Saddam Hussein captured two towns from a rival Kurdish group in fierce fighting Sunday. The groups gave conflicting accounts of whether Saddam's forces took part in the assaults.

Iraq, meanwhile, claimed it fired anti-aircraft weapons at U.S. and allied aircraft patrolling no-fly zones over its territory Sunday. The Iraqi fire missed and the planes fled, the official Iraqi News Agency said. Iraq made the same claim on Friday and Saturday, also saying there were no hits.American pilots have said they have detected no Iraqi response to their sorties.

In northern Iraq, the Kurdistan Democratic Party pressed ahead with its week-old offensive, marching east and taking the towns of Degala and Kuysanjaq from the Patriotic Union of Kurdistan.

Both groups agreed that the towns, 20 and 30 miles east of Irbil, changed hands amid heavy fighting.

But the KDP said in a statement from London that it launched the assaults on its own, while PUK spokesman Latif Rashid, speaking to The Associated Press from London, said the faction was overwhelmed by the combined forces of the Iraqi army and the KDP.

The Iraqi government said its forces were not involved. "We stress once again that our armed forces have already returned in full to their previous positions," an Information Ministry source told the state-run Iraqi News Agency.

No details of the fighting were available, and there was no word on casualties.

Iraqi forces teamed up with the KDP on Aug. 31 to capture Irbil, the de facto capital of the Kurdish safe haven established in northern Iraq after the 1991 Persian Gulf War.

The United States responded with missile attacks on southern Iraq on Tuesday and Wednesday, hammering air defense sites in southern Iraq.

Since then, the Iraqi forces appear to have refrained from playing a major role in the battles between the rival Kurdish groups.

But Iraq placed its heavy weaponry only a few miles behind the front-line positions of its KDP allies. Almost 100 Iraqi tanks could be seen in the region on Friday, and Defense Secretary William Perry, speaking on CBS' "Face the Nation," said Sunday that some Iraqi troops "are still nearby and still dangerous."

A United Nations officer in Irbil, speaking on condition of anonymity, said a force made up mainly of KDP fighters, but aided by some Iraqi government troops, was moving to the east on Sunday. He said the intense fighting prevented U.N. officials from going to the scene.

In Washington, Joint Chiefs of Staff Chairman Gen. John Shalikashvili told NBC's "Meet the Press" that Saddam "is clearly exploiting the difference between those two Kurdish factions."

But he said "very, very few" Iraqi troops were still in the safe haven area. "There continue to be reports of a few hundred here, a few hundred there."

The KDP said it was pushing east toward the Dokan Dam hydroelectric plant. The group said the PUK, which controls the plant, cut power and water to Irbil after being driven out a week ago. It said Irbil, a city of about 1 million, was suffering from "severe water and sanitation problems."

The offensive was also taking the KDP in the direction of Sulaymaniyah in the east, the last major stronghold of the PUK.

According to the Patriotic Union of Kurdistan, many families fled Kuysanjaq, a town of about 80,000, in response to Sunday's fighting.

The group appealed for "urgent and decisive" help from the United States and its allies.

But the Americans have made clear they do not want to take sides in Kurdish infighting. The missile attacks last week targeted southern Iraq, and Washington has taken no action in the north.

"We should not be involved in civil war in the north," Perry said. He said any retaliatory attacks would take place "where our interests are."

Shalikashvili said there are signs that Saddam is trying to repair the surface-to-air missile sites damaged in the U.S. raids.

"We have warned Saddam Hussein that any attempt to repair those sites or reinforce them will be taken very seriously," he said.

Washington also expanded the southern "no fly" zone this past week in conjunction with the missile strikes.

About half of Iraq, comprising wide swaths of both the north and the south, are off-limits to Saddam's aircraft.