* Opposition leader refuses offer of PM
* Crunch session of parliament set for Tuesday
* Leadership has warned of possible state of emergency
* U.S. asks government to work with opposition (Adds U.S. urging president not to declare state of emergency, paragraphs 5-6)
By Richard Balmforth and Natalia Zinets
KIEV, Jan 28 (Reuters) - Ukrainian President Viktor Yanukovich agreed in talks with opposition leaders to the repeal of some anti-protest laws and to discuss the fate of the current government at a crunch session of parliament on Tuesday, called to end two months of unrest against his rule.
But former Economy Minister Arseny Yatsenyuk, now a leader of the opposition, refused his offer of the prime minister's job, setting the scene for a tough political battle in parliament over opposition demands for concessions, including an amnesty for detained protesters.
There was no mention of any declaration of a state of emergency - something that Yanukovich's Cabinet ministers threatened to call for on Monday to re-establish control over the security situation in the country, where protesters are seizing public buildings.
Talk of a state of emergency being declared in the former Soviet republic of 46 million made the European Union's foreign policy chief, Catherine Ashton, hastily move up a visit to Kiev on Tuesday.
U.S. Vice President Joe Biden called Yanukovich on Monday to urge the government not to declare a state of emergency and to work with the opposition to bring a peaceful end to unrest.
"(Biden) underscored that the U.S. condemns the use of violence by any side, and warned that declaring a State of Emergency or enacting other harsh security measures would further inflame the situation and close the space for a peaceful resolution," the White House said.
After a four-hour meeting, Yanukovich's justice minister, who was at the talks with opposition figures, said they agreed to scrap parts of an anti-protest law 10 days ago that triggered violent protests from activists.
The minister, Olena Lukash, was quoted on the presidential website as saying the question of the government's "responsibility" would be discussed in parliament on Tuesday, suggesting there could be a vote of no-confidence in Mykola Azarov's government as a concession to the opposition.
But she said Yatsenyuk, one of a "troika" of opposition leaders, had formally refused to accept the prime minister's post offered to him by Yanukovich over the weekend.
Yanukovich triggered the upheaval in the sprawling country in November when he abruptly abandoned plans to sign association and free trade deals with the European Union. He opted instead to tighten economic ties with former Soviet master Russia, angering millions who dream of a European future.
The protest movement has since turned into a mass demonstration, punctuated by clashes with police, against perceived misrule and corruption under Yanukovich's leadership.
Several hundred people camp round-the-clock on Kiev's Independence Square and along an adjoining thoroughfare, while more radical protesters confront police lines at Dynamo football stadium some distance away.
Opposition leaders, who include boxer-turned-politician Vitaly Klitschko and nationalist Oleh Tyahnibok, have been pressing Yanukovich to repeal fully the anti-protest laws, dismiss the Azarov government and call early elections.
Yatsenyuk's refusal to accept the position of prime minister confirmed that the opposition regarded Yanukovich's offer as a trap that could divide them and undermine their credibility before the thousands of protesters on Kiev's streets.
Another battle lies ahead over protesters detained during the unrest. The Yanukovich side said these would be pardoned, but only once protesters had ended their occupation of public buildings and blockade of roads.
Yanukovich's Party of the Regions and its allies hold a majority in the Ukrainian parliament and pressure from the president and his aides behind the scenes can easily swing a vote the way he wants it to go.
But given the complexity of protesters' grievances and the anger on the streets, it seemed unlikely a clear-cut solution would emerge on Tuesday.
Six people have been killed in the unprecedented violence in Kiev that has set Russia and the West at loggerheads over the fate of the former Soviet republic.
Earlier, Lukash herself raised tensions by warning she would press for a state of emergency if protesters did not vacate a Justice Ministry building they had occupied overnight.
The protesters left the premises after several hours, but said they would return if there was no progress in parliament on Tuesday.
OPPOSITION RALLY CALL
The Batkivshchyna, or "Fatherland," party of jailed opposition leader Yulia Tymoshenko and now headed by Yatsenyuk, called on its supporters to rally in Independence Square on Tuesday in solidarity with opposition deputies in parliament.
"Come at 12 o'clock and support the deputies who are ready to take on themselves the responsibility for getting rid of these dictatorial laws," a statement said.
The occupation of the Justice Ministry building was the third such action in four days. Protesters occupied the Agricultural Ministry on Friday and only agreed to leave the Energy Ministry, which they entered on Saturday after the minister warned their action could disrupt energy supplies in the country.
Lukash said in a video statement, "If the Justice Ministry building is not vacated immediately, I will be forced to appeal ... to the Council for National Security and Defence with a demand that introduction of a state of emergency in the country be discussed."
A state of emergency would limit movements of people and vehicles, ban rallies, marches and strikes, suspend the activity of political parties and introduce a curfew.
The EU's chief Ashton, in a statement, said she was alarmed by the reports of a possible state of emergency being declared, which she said would "trigger a forward downward spiral for Ukraine."
Calling for the complete repeal of the anti-protest laws which Western governments say are undemocratic, she said she would visit Kiev on Tuesday.
The United States has warned Yanukovich that failure to ease the standoff could have "consequences" for its relationship with Ukraine. Germany, France and other Western governments have also urged him to talk to the opposition.
Russia has stepped up its warnings against international interference in Ukraine, telling European Union officials to prevent outside meddling and cautioning the United States against inflammatory statements. Russian President Vladimir Putin is due to visit Brussels on Tuesday for what promises to be a tense EU-Russia summit. (Additional reporting by Natalia Zinets and Adrian Croft in Brussels, and Robert Rampton and Jeff Mason in Washington; Writing by Richard Balmforth; Editing by Amanda Kwan, G Crosse and Peter Cooney)