"We may be short 12 or 13 seats to [achieve a] two-thirds [majority] but that will not be a challenge for us," Dullas Alahaperuma, the UPFA spokesman and transport minister, said.
"There is no question about the victory."
Al Jazeera's Prerna Suri, reporting from the capital Colombo, said voting was continuing in many districts of the country.
"The results show that about 65 per cent of these votes have gone to the ruling alliance," she said.
"The other 30 per cent has gone to the main opposition, the United National Party, and five per cent has gone to the JVP led by the former army chief Sarath Fonseka."
Around 14 million voters and more than 7,600 candidates from 36 political parties took part in the elections.
Fonseka, who was arrested in February on charges of sedition, has run his campaign for a parliamentary seat while in detention.
He was Rajapaksa's main challenger in the January presidential elections, the first such polls held since Sri Lanka defeated separatist Tamil Tigers last May.
Rajapaksa, who won the January election, has been looking to consolidate his power against an opposition movement that has been weakened and fragmented by Fonseka's arrest.
Voter turnout has been less than expected, however, hovering around 50 per cent of the electorate - Sri Lanka's lowest ever in a parliamentary poll.
Our correspondent said many people felt this was due to a "combination of factors, including voter fatigue".
The opposition has accused the UPFA of violating campaign rules and warned before the election that the vote would not be free and fair.
It accuses Rajapaksa of stifling dissent, encouraging cronyism and corruption and trying to establish up a family dynasty, with two of his brothers and a son running for parliament and other relatives occupying top government posts.
On the eve of voting Ranil Wickremesinghe, the former prime minister and leader of the main opposition United National Party (UNP), accused Rajapaksa of using state-owned vehicles and buildings for campaigning and turning the government-run media into a party mouthpiece.
"There was suppression of private media. Journalists were attacked and abducted by those connected to the government," he said.
Rajapaksa's government has denied the charges and claimed instead that the opposition was trying to curry favour with Western governments it accused of trying to undermine Sri Lanka.
Opponents have said Rajapaksa might seek a change that would allow him to stand for office beyond the current two terms allowed.
|Opposition parties have accused Rajapaksa, centre, of trying to stifle dissent [Reuters]
His political arch-rival, Fonseka, is being held in military custody awaiting court martial, but managed to campaign from his jail cell for a seat in Colombo, the capital.
Fonseka is accused of planning his political career before he gave up his army post and of breaching regulations in purchasing military hardware.
He has denied the charges, and while he remains a rallying cry for the opposition, his arrest has fragmented the opposition, with parties that had backed him in a single coalition fielding candidates separately in parliamentary elections.
Despite the end of the war and the Tigers' defeat, security remained tight for the vote.
At least 20,000 troops were placed on duty to support police personnel at polling stations around the country.