Secretary of State Condoleezza Rice urged Iraqi leaders on Tuesday to speed up national reconciliation on a trip overshadowed by an incursion by several hundred Turkish troops into northern Iraq.

About 300 Turkish soldiers, carrying only light weapons, entered an area of the mountainous northern Kurdish province of Dahuk, about 200 km (120 miles) from the Iraqi city of Kirkuk, where Rice's plane first touched down.

The soldiers clashed with Kurdish separatist guerrillas, a Turkish military official said. Turkey says it has the right to use military force to combat Kurdish rebels who shelter in the semi-autonomous Kurdish region of northern Iraq.

The incursion was a sharp reminder that while violence in Iraq has dropped by 60 percent since June, security is fragile and Iraq still faces threats both from within and without. The Kurdish Regional Government condemned the incursion.

Making her eighth visit as secretary of state, Rice was expected to pressure Prime Minister Nuri al-Maliki's Shi'ite-led government to break a political deadlock and reach an accommodation with minority Sunni Arabs and Kurds.

Security in Iraq has improved due to the deployment of an extra 30,000 U.S. troops, an uprising by Sunni Arab tribes against al Qaeda, and a six-month ceasefire declared by Shi'ite cleric and militia leader Moqtada al-Sadr.

But Maliki's government remains paralyzed by deep divisions and mistrust between leaders of Iraq's different religious sects and ethnic groups. It has made little headway in passing laws seen as vital to reconciliation.

What is missing here, and what is absolutely necessary over the long term to secure all of this, is political progress, State Department Iraq coordinator David Satterfield told reporters.

He said Rice's message to the Iraqi leaders would be that the country is coming together in bits and pieces and they had to cooperate to bring it together at a national level.

Washington dispatched the 30,000 extra troops earlier this year to help quell sectarian violence that has killed tens of thousands of Iraqis and to give Iraqi political parties breathing space to reach political consensus.

She is saying, look, see what's been done ... on security, on economics. You guys have got to catch up ... to solidify and to stabilize those other gains, Satterfield said.

As a helicopter carrying Rice and her entourage landed in Baghdad's heavily protected Green Zone, which houses the U.S. embassy complex and the Iraqi government, a car bomb exploded in central Baghdad just across the Tigris River, killing four people and wounding seven, police said.

Rice headed to President Jalal Talabani's residence, where she met several Iraqi leaders. Maliki was not expected to be among them but she planned to meet him later, officials said.

KIRKUK CRISIS

Rice first flew into Kirkuk, a mixed city of Kurds, Arabs and Turkmen 250 km (155 miles) north of Baghdad. The city is seen as the next powderkeg in Iraq, with Kurdish nationalists demanding it be included in their largely autonomous region.

Her decision to start her visit in Kirkuk appeared part of the new U.S. policy of focusing more on fostering reconciliation at a local and regional level. Kirkuk, with its huge oil reserves and potential for destabilizing violence, is key.

Iraq's minority Kurds, who control the largely autonomous Kurdistan region, see Kirkuk as their historical capital, but Arabs encouraged to move there under Saddam Hussein want it to remain under the sway of the Baghdad government.

A clause in Iraq's constitution provides for a referendum to be held there by December 31 to determine whether the area joins Kurdistan, but it has been delayed because of the deep divisions among Arabs and Kurds.

Rice met members of the local provincial council, whose work has been impeded because of boycotts by two major ethnic groups. Sunni Arab representatives recently ended their boycott and Turkmen are moving ever more steadily towards participation, Satterfield said.

Satterfield said the United Nations special representative to Iraq, Steffan de Mistura, had secured an agreement between the different parties in the past few days to allow the U.N. to play an enlarged role in moving the referendum process forward.

This is a very big step, he said.

(Writing by Ross Colvin; Editing by Elizabeth Piper)