Saakashvili needed a clean election to persuade sceptical European states that it is worth defying Russian objections and make Georgia a Nato member.
Results from 1,500 of around 3,500 precincts said Saakashvili's United National movement had more than 63 per cent of the vote.
In a statement, the Organisation for Security and Co-operation in Europe (OSCE), the continent's main election monitor, said: "Election day was overall calm and generally assessed positively. There were numerous allegations of intimidation some of which could be verified."
The monitors said the distinction between the state and the ruling party had often been blurred but that overall the election had expressed the will of the people.
Joao Soares, co-ordinator of the OSCE short-term observer team in Georgia, said: "These elections were not perfect but since I was here in January for the presidential elections concrete and substantial progress has been made. Problems and much work remain."
Dimitrij Rupel, the foreign minister of Slovenia, the current European Union president, said on Thursday that the reports from Georgia's elections were "encouraging" and showed the situation was better than in previous elections.
"The first evaluation of the elections are mostly positive although we still have to wait for the reports (of international observers)," Rupel said.
"There seems to be no doubt that Saakashvili's party has won.
"We all want a stable Georgia and we want things there to improve. It seems (that the situation) was better now than at the presidential elections (in January) and that is an encouraging result."
Saakashvili' predicted that his party could get close to a constitutional majority, or two-thirds of the seats, in parliament.
In an address to the nation on Thursday, Saakashvili said: "Yesterday was the triumph of the will of the Georgian people."
"No one can raise their hand against the will of the Georgian people. Even I was astonished by the big level of support which we got in these parliamentary elections."
But the opposition said voters had been intimidated by local officials and police and that the media had been dominated by coverage of the ruling party.
David Gamkrelidze, an opposition leader, said: "This was a criminal election. We together with the people must achieve the cancellation of the election results and the calling of a new parliamentary election."
Levan Gachechiladze, the main opposition coalition leader, had said that folowing the election 100,000 people would gather on the streets to claim victory for the opposition.
However, a protest on Thursday only attracted 4,000 people in central Tbilisi.
Saakashvili's democratic credentials were tarnished when he sent riot troops to crush protests against his rule last November.
He then won a snap presidential election in January which critics said was rigged, a claim he denied.
Wednesday's election has been overshadowed by tension over Russia's growing support for the Georgian separatist Abkhazia province.
A 20-minute shootout took place on polling day along the border between Georgia and Abkhazia.
A bus full of voters was attacked and several civilians were injured while attempting to vote.
The government blamed the attack on Abkhaz separatists.