Parliament in Ukraine has named its speaker as interim president.

Oleksandr Turchynov takes charge following the dismissal of President Viktor Yanukovych on Saturday. Mr Turchynov told MPs they had until Tuesday to form a new unity government.

Later, in a TV address, Mr Turchynov suggested Ukraine would re-open talks with the EU about closer links.

Mr Yanukovych's rejection of an EU-Ukraine trade pact triggered the protests that toppled him.

In his address, Mr Turchynov said he was "open to dialogue with Russia" as long as Moscow respected "Ukraine's European choice", according to translated remarks carried by the AFP news agency.

Meanwhile, opposition leader Yulia Tymoshenko, who was freed from jail on Saturday, has ruled out becoming prime minister again.

Her release was one of the conditions of the EU-Ukraine trade pact that Mr Yanukovych rejected last year.

Thousands of opposition supporters remain in Kiev's Independence Square, heeding opposition calls not to disperse.

The health ministry says 88 people, mostly protesters, are now known to have been killed in clashes since 18 February.

In response to reports that her name was being mentioned as a possible candidate, Ms Tymoshenko issued a statement reading: "No-one has agreed or discussed this with me.

"Thank you for your respect but I would like you not to consider my nomination for the post of the head of government."

Mr Turchynov, a close associate of Ms Tymoshenko, has described forming a unity government as a "priority task".

"We don't have much time," one of the opposition leaders, former world champion boxer Vitaly Klitschko, said as parliament began its debate.

Speaking to the BBC, he also suggested a bid for the presidency in elections scheduled for 25 May.

"I want to make Ukraine a modern European country," he said. "If I can do that through the president's position, I will do my best."

In other decisions on Sunday:

In an address on Saturday, Mr Yanukovych refused to officially stand down. He is last thought to have been in the eastern city of Kharkiv after travelling there late on Friday night.

Media reports have quoted Ukrainian officials as saying he was stopped by border police while attempting to fly to Russia aboard a private plane.

MPs from Mr Yanukovych's Party of Regions now appear to be disowning him.

"Ukraine was betrayed and people were set against each other. Full responsibility for this rests with Yanukovych and his entourage," its MPs said in a statement carried by Interfax-Ukraine.

International reaction to events in Ukraine has continued on Sunday, with US National Security Adviser Susan Rice warning Russia it would be a "grave mistake" to intervene militarily.

Russia and the US have been on opposite sides during the Ukraine crisis, which the US, along with the EU, backing the opposition.

"It's not in the interests of Ukraine or of Russia or of Europe or the United States to see a country split," Ms Rice told NBC.

There has been a fear that the crisis may exacerbate divisions between the Russian-leaning east of the country and the more pro-EU west.

Russian Foreign Minister Sergei Lavrov held his second conversation with US counterpart John Kerry in two days on the crisis, telling him that the opposition "had in effect seized power in Kiev, refused to disarm and continued to place its bets on violence," Reuters reports.

However, the US state department said Mr Kerry had told Mr Lavrov that the US was voicing "strong support for the action of the Ukrainian parliament today to name an acting president and acting prime minister".

Earlier, German Chancellor Angela Merkel was reported to have called Ms Tymoshenko and urged her to work for unity.

Mrs Merkel also called Russian President Vladimir Putin on Sunday to discuss the crisis; both agreed that the country's "territorial integrity must be safeguarded", her spokesman said.

Germany is trying to act as a broker in the conflict and to assuage Russian fears that it will be threatened if Ukraine moves closer to the European Union, the BBC's Stephen Evans reports from Berlin.

Some German government MPs have called for swift financial aid to Ukraine, possibly involving the International Monetary Fund, our correspondent reports.

Moscow recently agreed to provide $15bn (£9bn; 11bn euros) to support the Ukrainian government. If Russia withdrew that offer, the debate in Berlin is whether the European Union could replace the Russian money and how that might affect relations with Moscow, he adds.

EU foreign policy chief Catherine Ashton will visit Kiev on Monday to discuss EU support "for a lasting solution to the political crisis and measures to stabilise the economic situation",her office announced, external.

Earlier, a US official said US Treasury Secretary Jack Lew had discussed Ukraine with Russian Finance Minister Anton Siluanov on the sidelines of the G20 meeting in Sydney.

Mr Siluanov reportedly left open the question of whether Russia will pay the next instalment of financial help for Ukraine, worth $2bn.