President Mikheil Saakashvili's United National Movement won about 120 of 150 seats in parliament in the May 21 parliamentary polls. The United Opposition bloc, which received just 16 seats, has demanded that the president acknowledge the elections were rigged, and has called for the results to be annulled.
Manana Nachkebiya, representing the New Rightists political party in the United Opposition, said "Our alternative parliament will start its work simultaneously with the new parliament - on June 10 - if they manage to convene at all."
Opposition supporters have pledged to gather outside parliament on June 10, forming a human ring round the building, to block the first session.
Nachkebiya said the alternative parliament will be housed in the building of the New Rightists party, and will monitor all activities of the elected parliament.
"We will not allow the ruling party sit in parliament and do whatever it wishes," she said.
Tens of thousands of opposition supporters gathered in Tbilisi on Monday to protest against the results of the parliamentary polls, as Georgia held a military parade to mark Independence Day.
President Saakashvili has so far rejected the opposition's demands for an annulment of the results, saying: "We will not tolerate the language of ultimatums. The people of Georgia has already made its choice and elected parliament, and it will start work in compliance with existing procedures."
Tbilisi saw six days of mass opposition rallies last November, with protesters demanding Saakashvili's resignation over allegations of corruption and increasing authoritarianism.
International observers said the recent Georgian election had flaws but that the results reflected the overall will of the people.
Joao Soares, coordinator of the Organization for Security and Cooperation in Europe's 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."
