Thousands of protesters remain camped in Kiev's main square, despite attempts by the security forces to move them.
The presidency announced that a deal had been reached with the opposition after talks went on through the night.
It gave no details, but said the deal would be signed later.
There is no confirmation by the opposition.
Earlier in the crisis, opposition leaders refused to agree any deals with the government until they were approved by the protesters.
The talks were brokered by French, Polish and German foreign ministers.
On Thursday, EU foreign ministers said in a statement sanctions would be put on some officials over the violence.
The US has warned Kiev that it would follow suit.
Thursday was the bloodiest day since the unrest began in November, with many of the anti-government protesters reportedly killed by police snipers.
In all, 77 people - including policemen - have been killed since the violence first flared up on Tuesday, Ukraine's health ministry said.
Another 577 were injured.
Protesters had captured 67 police, the interior ministry said.
A number of them were later released.
'Forces of peace'
On Thursday, the foreign ministers of France, Poland and Germany conducted several hours of discussions with Mr Yanukovych on a "roadmap towards a political solution" before going on to talks with opposition leaders.
They returned for another meeting with Mr Yanukovych in the evening and the talks continued late into the night.
Polish Prime Minister Donald Tusk said Mr Yanukovych had expressed willingness to hold early elections this year.
Mr Yanukovych's aide Hanna Herman was later quoted as saying that the president was ready to make concessions to "restore peace".
She added that "forces of peace" among presidential advisers defeated the "hawks".
The snap presidential and parliamentary elections are one of the key demands by Maidan activists and opposition leaders.
Currently, the presidential poll is scheduled for next year.
Also on Thursday, the statement from an emergency EU foreign ministers' meeting in Brussels said "no circumstances can justify the repression we are currently witnessing".
EU foreign policy chief Catherine Ashton said the "prime responsibility" to get talks between the two sides under way lay with President Yanukovych.
She said ministers had expressed their "dismay" at the latest violence and had agreed to "suspend export licences for equipment for internal repression".
Implementation of the measures "will be taken forward in light of developments in Ukraine", she added.
The EU had until now refrained from imposing sanctions, preferring to emphasise dialogue and compromise.
US Vice President Joe Biden also warned President Yanukovych in a telephone conversation that Washington was ready to impose sanctions against Ukrainian officials guilty of ordering troops to fire on protesters.
The US state department had already announced visa bans on 20 members of the Ukrainian government but has not provided any names.
Dozens of protesters were killed by security forces in Kiev on Thursday following the breakdown of a truce the previous day.
Activists and doctors working in protester camps suggested the death toll could be as high as 100 and would rise further.
A number of bodies of protesters killed on Thursday were brought to the Maidan (Independence Square), the BBC's Duncan Crawford in Kiev reports.
Assembled crowds shouted "Martyrs!" and "Heroes!", with some protesters in tears, our correspondent adds.
Witnesses have told the BBC that some of those killed died as a result of single gunshot wounds, typical of sniper fire.
Video footage has emerged apparently showing snipers firing on demonstrators who had been trying to retake their protest camp in Independence Square.
The authorities said one policeman had died, however an activist reported that as many 10 police officers had been killed.
Officials said more than 20 policemen had also been injured.
Witnesses reported live rounds, petrol bombs and water cannon being used at Independence Square during Thursday morning's clashes.
Some armed demonstrators were also reported to be firing towards security forces.
Gunshots pierced the windows of rooms at the Ukraina Hotel, which is serving as the base for all foreign media in Kiev, including the BBC.
A statement on the presidential website blamed the opposition for starting the violence, saying the "calls for a truce and dialogue were nothing but a way of playing for time to mobilise and arm militants from Maidan".
MPs assembled for a session of parliament on Thursday afternoon voted to condemn the recent violence.
They also called for the use of weapons against protesters to be banned, and for troops and police deployed against them to be withdrawn.
The session was attended by 239 out of 450 MPs, most of them from opposition parties.
But there were also dozens from the pro-Presidential Party of Regions.
The protests first erupted in late November when President Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Source: BBC News