U.S. officials warned Saddam Hussein to keep his distance from Kurdish rebels Thursday as the Kurds advanced slowly on Irbil, the main city in northern Iraq.

Only Irbil now stands between the fighters of the Iran-allied Patriotic Union of Kurdistan and a convincing victory over their Saddam-backed rival, the Kurdistan Democratic Party.

Having pulled within striking distance, the PUK opted not to close in, since Iraqi tanks and troops were dug in southwest of the city. Residents said Irbil was calm Thursday, although skirmishes continued 20 miles outside the city.

In Washington, State Department spokesman Nicholas Burns said any decision by Saddam to intervene in the Kurdish dispute would be a “grave mistake.” He issued a similar warning to Iran.

“We’re calling up on Iraq and Iran to stay out of the fighting in northern Iraq, not to inflame it, not to engage in any provocative behavior that will just lead to further instability and further violence,” Burns said.

Iraq, Iran and the United States are pressing for peace talks. Assistant U.S. Secretary of State Robert H. Pelletreau plans to travel to the region this weekend to meet with Kurdish leaders.

Irbil has been held by KDP forces since Aug. 31, when they captured it from the PUK with the help of Saddam’s army. Saddam’s intervention prompted U.S. retaliation with cruise missile attacks on Iraqi airdefense systems in southern Iraq.

KDP leader Massoud Barzani threatened Thursday to seek more support from Saddam.

“If we need, we’ll ask Iraq to help us again,” Barzani told reporters in Salah ad Din, 20 miles northeast of Irbil. “Our enemy is Iran. PUK is a puppet.”

The PUK was moving toward the city from the east and northeast, coming closest to Irbil in the village of Banawiyeh, 20 miles to the northeast.

“We are not advancing because Saddam’s tanks are protecting Irbil,” said a front-line PUK guerrilla who did not want to be named.

But Mokaddar Kawakawani, an officer with the rival KDP, said his opponents were not advancing because they did not have the strength to do so.

A PUK statement Thursday said elite Iraqi Republican Guards were moving toward Irbil from Baghdad, to support Iraqi tanks encamped 30 miles south of the city. There was no confirmation, however, of any movement by Iraqi forces.

The two Kurdish factions long have fought to control northern Iraq, which the United States and its allies set up as a “safe haven” in 1991 to protect the Kurds after their failed uprising against Saddam.

In Sulaymaniyah on Thursday, the area’s second-largest city, a PUK victory celebration looked no different than the one held when the rival group took over in August. The PUK regained control of the city Sunday.

“One comes, one goes. We’re used to our town changing hands,” said Marivan Abdurrahman, a 26-year-old clothing salesman.

Residents said there has been little bloodshed along with the changes.