Russia has urged Ukrainian opposition leaders to end their campaign of "ultimatums and threats" and to step up negotiations with the government.
Russia's foreign ministry said Moscow was concerned by activists' attempts to "inflame" the situation.
Protesters in Kiev have repeated their calls for the resignation of President Viktor Yanukovych, who is now back at work after four days of illness.
The EU and US are considering a big loan to help debt-laden Ukraine.
Continue reading the main story
Analysis
image of David Stern
David Stern
BBC News, Kiev
Western officials for the most part have followed a policy of reaction in dealing with events in Ukraine, ever since President Viktor Yanukovych's surprise cancellation of landmark agreement with the EU unleashed the anti-government Euromaidan movement.
Now, however, Washington and Brussels seem to have taken the initiative. A prospective joint EU-US financial aid package, announced in the Wall Street Journal, is intended to encourage reforms and a peaceful resolution in the country's protracted political standoff.
It's an understatement to say that the plan depends on a number of variables. President Yanukovych's acceptance of the plan - if it is offered - is one of the main ones. Another is the reaction to the protesters on Kiev's streets, who might not welcome the possibility of a "national unity" government, which leaves Mr Yanukovych in power.
It's a "big carrot," one senior US official was quoted as saying. The next weeks will show if it is indeed what is needed.
"We are looking at how we could support the Ukraine in the times of the crisis when it comes to the economic and political situation," a spokeswoman for EU foreign policy chief Catherine Ashton said on Monday.
Both EU and US officials say the aid package would be conditional on Kiev embracing "real reform".
No further details of the plan have been revealed.
'Deep crisis'
Protests have continued since November, when President Yanukovych backed away from closer EU ties and agreed a loan with Russia.
Thousands of people joined a new rally in the centre of the capital, Kiev, on Sunday, with opposition leaders calling for international help.
The Russian foreign ministry denounced their actions in a statement on Monday, saying they were particularly "puzzling" in the wake of a summit held in Munich last week on Ukraine's future.
"We expect the opposition in Ukraine to avoid threats and ultimatums and step up dialogue with the authorities in order to finding a constitutional way out of the country's deep crisis," the foreign ministry said.
A street vendor sells flags of Ukraine and EU in Maidan Square in Kiev on 3 February 2014.
Protesters want to see closer ties with the EU rather than Russia
Anti-government protesters take part in a demo in Kiev on 2 February 2014
Activists gathered in freezing conditions in Kiev's Maidan square on the eve of the president's return to work
Russia has announced it is delaying the next instalment of a $15bn (£9bn) aid package to the Ukraine.
The next tranche is dependent on the formation of a new Ukrainian government, it says.
Concessions
President Yanukovych's first task on returning to work is to name a new prime minister to replace Mykola Azarov who resigned last week.
On Tuesday, the Ukrainian parliament will debate calls for a broader amnesty for people detained during the protests and for a return to a previous constitution, which will restrict the powers of the presidency.
Mr Yanukovych had been on sick leave since last Wednesday. His office said he had been suffering from a fever and breathing problems.
Opposition leaders had previously expressed scepticism about his illness - on Sunday they again called on him to stand down while speaking to crowds of protesters in Kiev's Maidan square, which has become a focal point for the opposition.
Mr Yanukovych has offered a number of concessions and his cabinet quit their jobs.
But the demonstrators, many of whom want to see closer ties with the EU rather than Russia, have not been placated.
Meanwhile, the severely injured Ukrainian opposition leader Dmytro Bulatov has arrived in Lithuania for medical treatment.
Mr Bulatov appeared on TV last week saying he had been abducted and tortured.
Connect With Us