However, it said that overall the vote had expressed the will of the people.
The president's democratic credentials have been under intense scrutiny after he used riot police to crush protests against the government last November.
The demonstrators also allege that he rigged his presidential victory in January.
Opposition deputies tried to enter the parliament building on Monday but were barred by special service soldiers.
Koba Davitashvili, a former Saakashvili ally who is now an opposition leader, called for the president to recognise the vote had been rigged.
"If Saakashvili does not recognise the election as falsified then the people will move towards the place where he currently sits and demand an answer from him," Davitashvili told the crowd.
The opposition said over 100,000 had gathered for the protest, but international journalists at the rally put the figure at 40,000.
The lower figure would still make it the biggest protest demonstration since Saakashvili's January inauguration.
Most of the protesters gathered for the rally after attending Georgia's annual Independence Day military parade, at which Saakashvili was present.
Addressing the crowd, Salome Zurabishvili, an opposition leader who once served as Saakashvili's foreign minister, said: "We want these elections to be cancelled and we want this parliament to be abolished."
Some protesters carried an effigy of Saakashvili with a banner saying "Vote Thief" while others chanted "Misha go! Misha go!" Misha is a short form for the name Mikheil.
|Saakashvili wants to convince the West of his|
democratic values in order to join Nato [ETA]
Opposition leaders, who have vowed to boycott the new parliament, said they would prevent parliament from convening next month by forming a human cordon around it.
"We won't allow a new parliament to gather and to start working," David Gamkrelidze, a leader of the opposition bloc which took second place in the elections, told the rally.
Saakashvili has been hoping to portray the elections as fair as part of his plan to convince the West to defy Russian objections and offer Georgia Nato membership.
Dmitry Medvedev, Russia's president, sent congratulations to Saakashvili for the Independence Day celebrations and said Moscow wanted good relations with Tbilisi.
Georgia has accused Russia of supporting its breakaway regions of South Ossetia and Abkhazia.
On Monday, the United Nations released a report saying that a Russian fighter plane had shot down a Georgian drone last month over Abkhazia.