TBILISI, Georgia — The ruling party and an opposition coalition both claimed victory yesterday in a parliamentary election in this former Soviet republic, after a campaign colored by escalating tensions with neighboring Russia.

During the election, widely seen as a test of Georgia’s young democracy, voters from a separatist territory were apparently fired upon on their way to the polls.

But in the capital, Tbilisi, polling stations were calm. With international observers watching the process, citizens cast ballots 4 1/2 months after a presidential vote that gave American-educated Mikheil Saakashvili a second term in office, but that some foreign monitors called flawed.

Exit polls yesterday showed the United National Movement, Saakashvili’s party, winning more than 63% of the vote, followed by the United Opposition Party, with about 14%, the Christian Democrat Party, with about 9%, and the Labor Party, with about 5%.

United Opposition leaders held a protest rally Wednesday night in Tbilisi, accusing the ruling party of stealing the vote. Their own exit polls, they said, tentatively showed the party with 42% of the vote.

They publicly called on party members to remain calm and go home pending official results.

The last year has been politically turbulent for Georgia. In November, riot police beat anti-Saakashvili demonstrators and closed down an opposition television station, leading to international criticism and the snap presidential election in January.

This spring, the NATO alliance denied Georgia and Ukraine an action plan for eventual membership.

Many Georgians believe that decision emboldened Russia to beef up its military presence in Abkhazia.