It is unclear where the shots are coming from or whom they are targeting.
The Interior Ministry accuses the opposition of breaking a shaky truce and firing at law enforcement officers.
The new shots came after the deadliest day of violence in Ukraine since its independence from the Soviet Union, and amid tensions in parliament as lawmakers and European officials try to find a solution to the crisis.
Earlier Friday, Ukrainian presidency said it has negotiated a deal intended to end violent battles between police and protesters that have killed scores and injured hundreds, but European mediators involved in talks wouldn't confirm a breakthrough.
Yanukovych's office said that the government and the opposition have agreed to sign the deal at noon local time, but wouldn't give any details.
Yanukovych and the opposition are locked in a battle over the identity of Ukraine, a nation of 46 million that has divided loyalties between Russia and the West.
Several regions in the west of the country are in open revolt against the central government, while many in eastern Ukraine back the president and favour strong ties with Russia, their former Soviet ruler.
The demonstrators, who have camped for three months on Kiev's Independence Square, known as the Maidan, are demanding Yanukovych's resignation and early elections.
The president, who triggered the protests by aborting a pact with the European Union in favour of close ties with Russia, has made some concessions, but has refused to step down.
Ukraine has cancelled its planned issue of five-year Eurobonds worth $2 billion, the country's finance ministry said on Friday in a statement to the Irish Stock Exchange, reported Reuters.
The report of a deal between the presidency and the opposition followed the worst violence yet in the confrontation between the government and protesters.
Protesters advanced on police lines in the heart of the Ukrainian capital on Thursday, prompting government snipers to shoot back and kill scores of people in the country's deadliest day since the breakup of the Soviet Union a quarter-century ago.
Dr. Oleh Musiy, the medical co-ordinator for the protesters, said at least 70 protesters were killed Thursday and over 500 were wounded.
The Interior Ministry said three policemen were killed and 28 suffered gunshot wounds.
A statement on the website of the Health Ministry said 77 people had been killed between Tuesday morning, when the violence began, and Friday morning.
The statement said 577 people had been wounded and 369 hospitalized.
There was no way to immediately verify any of the death tolls.
EU diplomats urge caution on alleged deal European diplomats, who were involved in the talks between Yanukovych and the opposition that went on for hours Thursday and continued into the night, urged caution and said they could not confirm an accord had been reached.
A German official in Kiev said the talks were continuing.
A French official said it may be too early to call it an accord.
Both spoke on condition of anonymity because they were not authorized to be publicly named according to government policy.
French Foreign Minister Laurent Fabius, who was involved in the talks along with his German and Polish counterparts, said on Europe-1 radio Friday that "as long as things are not effectively completed, we must remain very prudent."
"The opposition wants to consult a certain number of its supporters, which is understandable," he said.
"We discussed all subjects during these negotiations. It was done in an extremely difficult atmosphere, because there were dozens of dead and the country is on the verge of civil war."
A lull in fighting appeared to hold on Friday morning, as several thousand protesters milled around the Maidan, and volunteers walked freely to the protest camps to donate food and other packages.
Support for the president appeared to be weakening, as reports said the army's deputy chief of staff, Yury Dumansky, was resigning in "disagreement with the politics of pulling the armed forces into an internal civil conflict."
Late on Thursday, the Ukrainian parliament passed a measure that would prohibit an "anti-terrorist operation" threatened by Yanukovych to restore order, and called for all Interior Ministry troops to return to their bases.
Yanukovych’s position was looking increasingly difficult, especially after the resignation of Lieutenant-General Yuri Dumansky, deputy head of the armed forces general staff.
“The armed forces of Ukraine are being drawn into a civil conflict. This could be the cause of a large number of deaths of civilians and servicemen,” Dumansky told Channel 5 television.
“I have decided to tender my resignation to avoid an escalation and bloodshed.”
Standard & Poor’s said the political situation in Ukraine had deteriorated substantially and this raised uncertainty about the financial aid promised by Russia under a $15-billion bailout package needed to help Kiev repay huge debts.
The second installment, of $2-billion, is expected to be paid soon but Moscow has signalled that Yanukovych must first restore order in the country of 46 million to get it.
“We consider that the future of the current Ukrainian leadership is now more uncertain than at any time since the protests began in November 2013,” the ratings agency said.
Earlier this month, bugged and leaked diplomatic phone calls exposed EU-U.S. disagreement on Ukraine.
Yanukovych has refused to consider calls to hold an early election, a year before his term is due to end.
In Kiev, demonstrators on Independence Square held a vigil after dark on Thursday for fallen comrades, lit by mobile phone screens held aloft.
Medics carried bodies on stretchers through lines of protesters who chanted “Heroes, heroes” to the dead.
Though armed militants on the barricades tend to be from the far-right fringe, the opposition has broad support.
But many Ukrainians also fear violence is slipping out of control.
Kiev residents emptied bank machines of cash and stockpiled groceries, with many staying off the streets.
In further signs of faltering support for Yanukovych, his hand-picked head of Kiev’s city administration quit the ruling party in protest at the bloodshed.
In an indication that Yanukovych is also losing support in parliament, the assembly late on Thursday adopted a resolution urging authorities to stop shooting, withdraw police from the centre of Kiev and end the action against the protesters.
But core loyalists were still talking tough. Interior Minister Vitaly Zakharchenko said on Thursday police had been issued with combat weapons and would use them “in accordance with the law” to defend themselves.