The opposition renewed its criticism of what it said were Wednesday's rigged elections, and some leaders called for a rally on Monday.
But an opposition rally on election-night drew only a few thousand people, casting doubt on their ability to muster the kind of large, sustained protests that could force political change.
The Organisation for Security and Co-operation in Europe (OSCE), Europe's main election monitor, said there had been "numerous allegations of intimidation some of which could be verified".
"These elections don't reflect the people's choice and the people's will. We are not recognising the results," David Gamkrelidze of the opposition New Rights party said.
"The opposition is seriously considering the possibility of boycotting the new parliament."
Georgia's new foreign minister acknowledged the parliamentary election had been imperfect despite efforts by the government to ensure a free and fair vote.
"It would have been impossible to do [things] in a really perfect way in terms of all European standards, but then the core importance we attach to this election was that everything had been done ... by the government to ensure the elections would be free and fair," Eka Tkeshelashvili said.
But Tkeshelashvili, who met EU officials in Brussels on Friday, said allegations of irregularities would be properly addressed and said she was optimistic about the new parliament, despite the opposition's threats to boycott proceedings.
A number of EU states rallied to Saakashvili's side, with Dimitrij Rupel, Slovenia's foreign minister whose country currently holds the EU's presidency, describing the vote as "encouraging".
Benita Ferrero-Waldner, the EU commissioner for external relations, said the elections showed "substantial progress".
Saakashvili has been praised as a reformer since coming to power in 2004, but was criticised last November after sending riot police to suppress an opposition protest, shutting a critical television station and briefly imposing emergency rule.
The elections were closely watched in Europe as Georgia has sought Western support in its stand-off with Russia over the breakaway Georgian regions of Abkhazia and South Ossetia.
Saakashvili earlier said Georgia had come close to war in its dispute with Russia over the separatist territories.
Analysts say the reasons behind the dispute are Saakashvili's pro-Western policies and plans to join Nato.