The Union of Right Forces, known as SPS, secured 0.9% of the internationally criticized December 2 vote, which saw an overwhelming victory for the pro-Kremlin United Russia party. The threshold for the lower house of parliament was set at 7%.
"I bear full responsibility [for the defeat] and am stepping down," Nikita Belykh said at a party congress.
Belykh questioned the election results cited by election authorities, but admitted the party's and his personal failure to "forge a united democratic front" ahead of the polls.
He said all members of the party's governing council would also resign, and invited the congress to consider Boris Nemtsov, an ex-deputy prime minister and a former SPS leader, as the party's candidate in presidential elections on March 2, 2008.
But Anatoly Chubais, head of the electricity giant Unified Energy System and a member of the SPS governing council, said the party should not accept Belykh's resignation.
Chubais said it was a "courageous move," but it was "absolutely ill-timed." He said the party should review its strategy and objectives not to repeat previous mistakes.
He also doubted whether Nemtsov, a fierce advocate of Russia's privatization camapaign during the turbulent 1990s, would be successful as a presidential contender.
Other opposition candidates to challenge United Russia's nominee, First Deputy Prime Minister Dmitry Medvedev, in the presidential polls are Soviet dissident Vladimir Bukovsky and ex-Prime Minister Mikhail Kasyanov, who have already been formally put forward by their action groups.
Medvedev, who enjoys President Vladimir Putin's backing, is widely seen as a front runner.
Kommersant daily quoted Bukovsky on Monday as saying he had signed a deal with Kasyanov and Nemtsov to coordinate activities in the run-up to the elections.
All of them will attempt to collect the 2 million signatures required to support their application and then get registered with the Central Election Commission, but the one with the highest rating will run as a single opposition candidate, the paper said.
