The ruling Democratic Party (DPJ) is struggling to enact legislation in the divided parliament, where opposition parties control the upper house and can block bills. The current session of parliament was due to end on June 22.
The party's second most senior figure, Katsuya Okada, said it planned to submit a "compact" extra budget in mid-July, followed by a bigger extra budget, also for reconstruction. Both budgets would come on top of one for 4 trillion yen ($50 billion) approved early last month.
"It would be unthinkable to close parliament and take a summer break while we are dealing with the disaster," Okada, the DPJ secretary-general, said in a speech to a union group.
"We need a big extension of the parliament session to debate and pass necessary bills."
Finance Minister Yoshihiko Noda said on Tuesday that the government would avoid issuing extra bonds to finance the second extra budget, which aims to cover areas including those related to the nuclear crisis triggered by the disaster.
Okada agreed with the party's parliamentary affairs chief that the session should be extended for three months, Jiji news agency reported. Still, the party faces a tough fight in the split parliament.
Opposition parties have refused to cooperate with the DPJ on policies while Prime Minister Naoto Kan is in power, clouding the outlook for key bills such as one needed to finance 44 percent of this fiscal year's $1 trillion budget.
They are also pressing the ruling party to drop some of its other spending plans.
Politicians are also at odds over a draft law to help Tokyo Electric Power Co pay billions of dollars in compensation to refugees from around its Fukushima Daiichi nuclear plant, where the quake and tsunami triggered radiation leaks.
Kan has promised to step down once the worst of the nuclear crisis is over, but has not made the timing clear, upsetting both the opposition and critics within his own party. ($1 = 80.440 Japanese Yen)