Ukraine's new interim President Oleksandr Turchynov has said the country will focus on closer integration with the EU.
Mr Turchynov was appointed following the dismissal of President Viktor Yanukovych by MPs on Saturday.
Mr Yanukovych's rejection of an EU-Ukraine trade pact triggered the protests that toppled him.
Russia, which had backed Mr Yanukovych, has recalled its ambassador to Ukraine for consultations.
Earlier Russian Foreign Minister Sergei Lavrov said the opposition "had in effect seized power in Kiev, refused to disarm and continued to place its bets on violence".
The US has said parliament's actions were legitimate and has warned Russia against military intervention.
Mr Turchynov, a close ally of former Prime Minister Yulia Tymoshenko, gave a televised address late on Sunday, hours after his appointment as interim president.
He vowed to set up a "government of the people", and said: "We have to return to the family of European countries."
He added: "We are ready for a dialogue with Russia... on a new, fair, equal and neighbourly basis, acknowledging and taking into account Ukraine's European choice."
European Union foreign policy chief Catherine Ashton has announced she is visiting Kiev on Monday to discuss EU support "for a lasting solution to the political crisis and measures to stabilise the economic situation".
Mr Turchynov said MPs had until Tuesday to form a new unity government.
Thousands of opposition supporters remain in Kiev's Independence Square, heeding opposition calls not to disperse.
The health ministry says 88 people, mostly anti-Yanukovych protesters, are now known to have been killed in clashes that took place earlier this week.
In an address on Saturday, Mr Yanukovych refused to 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 flee to Russia.
MPs from Mr Yanukovych's Party of Regions now appear to be disowning him, having issued a statement criticising him to Interfax-Ukraine.
Meanwhile Ms Tymoshenko, who was freed from detention 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.
Former world champion boxer Vitaly Klitschko suggested to the BBC that he may make 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:
- Foreign Minister Leonid Kozhara and Education Minister Dmytro Tabachnyk were dismissed
- Arrest warrants were issued for former Incomes Minister Oleksandr Klimenko and former Prosecutor-General Viktor Pshonka
- Parliament lowered the official status of the Russian language by cancelling a law brought in by Mr Yanukovych
- Parliament also voted to seize Mr Yanukovych's luxury estate near Kiev, which protesters entered on Saturday
Also on Sunday, US National Security Adviser Susan Rice warned Russia it would be a "grave mistake" to intervene militarily.
Russia and the US have been on opposite sides during the Ukraine crisis, with the US, along with the EU, backing the opposition.
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.
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.
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.
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.