KIEV, Ukraine -- Ukraine's president gave in to pressure from European diplomats and offered concessions Friday to defuse a crisis that has divided his country and left scores dead. Shots rang out near the protest camp and a skeptical opposition massed in central Kiev, divided over what to do next.

The capital remained tense after President Viktor Yanukovych announced early presidential elections and promised to bring opposition members into the government - but didn't say when.

CBS News correspondent Holly Williams reports from Kiev that there were scuffles Friday morning in Ukraine's Parliament as opposition members called for snap presidential elections. The protesters in Kiev's Independence Square told CBS News that they were staying put until Yanukovych was removed from power.

European foreign ministers had stayed up all night in Kiev trying to negotiate an end to the standoff, prompted when the president aborted a pact with the European Union in November in favor of close ties with Russia instead.

Small groups of protesters advanced toward the president's office, torching one truck and seizing two others. Scuffles broke out between a few dozen radicals who wanted to attack the building and more moderate protesters.

A group of police officers from western Ukraine arrived on Independence Square to show their support for the opposition, and one told The Associated Press that they had arms.

Yanukovych gave no time frame for new elections, and it's unclear whether his belated concessions will be enough to satisfy protesters who have occupied a piece of Kiev and government buildings around the country in a nationwide battle over the identity of their country.

The U.S., Russia and European Union are deeply concerned about the future of Ukraine, a nation of 46 million that has divided loyalties between Russia and the West. Shots rang out again Friday near the protesters' camp in Kiev, a day after the deadliest violence in Ukraine's post-Soviet history. It is unclear who was targeted and whether anyone was hurt or injured in Friday's incident.

As the president of Ukraine and the guarantor of the Constitution, today I am fulfilling my duty before the people, before Ukraine and before God in the name of saving the nation, in the name of preserving people's lives, in the name of peace and calm of our land, the president said in a statement on his website.

Yanukovych also promised constitutional reforms trimming presidential powers, a key demand of protesters.

The opposition has rejected similar invitations to join the government in the past, saying that constitutional reform giving parliament greater powers has to be passed first.

On the early elections, a Yanukovych ally earlier said that they would be held in December instead of March - not soon enough for many protesters enraged by police violence.

Lawmaker Inna Bogoslovskaya, allied with the opposition, told the AP that December is too late for elections. After 77 corpses yesterday ... that changes the stakes, she said. The Maidan (protest movement) demands immediate resignation of the president instead of early elections.

Protesters will not abandon occupied buildings until after the constitution is changed, she added.

Polish Foreign Minister Radoslaw Sikorski, who is involved in the negotiations in Kiev, called for calm and said he was going to meet with protesters on the Maidan. He tweeted that it's a delicate moment for the settlement and all must remember you don't get 100 percent in a compromise.

The German Foreign Ministry tweeted that Foreign Minister Walter Steinmeier and Sikorsky were to hold more talks with opposition leaders and protesters Friday.

All this was not enough for some protesters, who accused the president of trying to buy time and want him out immediately.

We don't believe him. He has cheated the people before. He declared a truce, and then there was shooting, said Valentin Mashul, manning a table with a collection box for money donations for the protesters.

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