Party heavyweights have blocked moves to oust him but agreed that Aso would appear before LDP legislators in meeting on Tuesday.
That gathering was closed to media in what many interpreted was a sign the party feared exposing its deep divisions.
Speaking after the meeting, Aso apologised for his failings and admitted that the party's internal chaos had contributed to recent local election losses.
"I am firmly resolved that we will sincerely accept the people's feelings, will and criticism and start afresh," he said, vowing to stay in his post until the economy recovered.
|Aso apologised for his failings but vowed to fight on [Reuters]
The LDP has ruled Japan almost without interruption for the past five decades.
Yoichi Masuzoem Japan's health minister, said all cabinet members, including Kaoru Yosano, the finance minister who some had earlier speculated might refuse to back Aso's election plan, backed him on Tuesday.
LDP legislators have stifled their criticism of Aso - at least for now - as they gear up for election battle.
"At this point we have no choice but to be united before the election," Hiroshige Seko, an upper house legislator, told reporters.
But Aso still faces an uphill task in trying to keep his job and his party in power.
The premier survived a no-confidence motion in parliament last week due to the LDP's dominance in the current house, but the latest newspaper polls indicate that dominance is about to end.
A poll published in the Mainichi newspaper puts the main opposition Democratic Party of Japan (DPJ) ahead of the LDP by a two-to-one margin.
Fifty-six per cent of voters indicated they would choose the DPJ and 23 per cent said they would vote LDP, according to the poll.
Another poll by Asahi newspaper showed similar results, with 49 per cent of respondents supporting the Democrats, and only 22 per cent behind Aso's party.
Yukio Hatoyama, the Democratic party leader, told party members on Tuesday to face the election with "a sense of historic mission".
"This is a major, revolutionary election to allow politicians to take the lead in Japanese government," he said.