Mironov first proposed to the Communist leader Gennady Zyuganov that the two parties unite on Sunday. Mironov also said his party would launch coalition talks with a number of leftist parties this week.
"I am again offering the leaders and Communist Party members to join forces under the Social Democrat banner," Mironov told a briefing on Monday.
Results after 98% of the vote had been counted show the pro-Kremlin United Russia party, whose candidate list was headed by President Vladimir Putin, has won with 64.1%. The Communists received 11.6%, which Mironov called a defeat.
"It is clear that they expected another result, which explains the emotional rejection by Gennady Zyuganov to unite," Mironov said.
Latest reports quoted Pavel Shcherbakov, an aide to the head of the Communists' election headquarters, as saying his party categorically refused to unite with A Just Russia.
"This option is not being considered. Regardless of how many seats the Communist party has in the next Duma, it will remain the only opposition force and does not plan to unite with the 'Kremlin project'," Shcherbakov said.
The Communist activist denied allegations of an aging communist electorate, saying their average voters were people of all ages, provided they are "educated and have access to media other than TV."
"We see no point in reacting to Mironov's proposals, as we consider his party phony," Shcherbakov said describing A Just Russia's results in the polls as "false" and contesting its own results.
Mironov also criticized a joint statement by the Organization for Security and Co-operation in Europe (OSCE) and the Council of Europe that Sunday's poll "was not fair and failed to meet many OSCE and Council of Europe commitments and standards for democratic elections."
"Let them look at what they've got themselves in the United States, this citadel of democracy, and in other countries," Mironov said.
He accused the OSCE of having formed the opinion that "all Russian processes are unlawful," long before December 2.
However, Mironov admitted that the suspiciously high voting looked abnormal. Ramzan Kadyrov, the President of Chechnya, for example claimed that 99 per cent of people had voted.
"The over 90% vote the United Russia party received in a number of Russian regions reminds me of the Communist times," Mironov said simultaneously alleging "a high confidence in local governments."
The leader of A Just Russia also said his party could support the candidate to be nominated by the movement of Putin's supporters.
"If the new movement nominates its candidate, our party will carefully consider him," Mironov said.
He added that A Just Russia would decide whether to nominate its own presidential candidate or support the nominee of another political party at a congress on December 25.