Defence Minister Stephen Smith says the government is going through a "tough time", but Prime Minister Julia Gillard remains the best leader for Labor.
Mr Smith, who has been mentioned in media reports as a potential leader, told reporters in Canberra on Monday there was "no vacancy".
"I am a very strong supporter of the prime minister," Mr Smith said.
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"There's no point other than acknowledging that we are going through a tough time.
"That always happens to a government when you are seeking to effect big reforms and that's what we are doing."
Mr Smith said the prime minister was taking a "long-term view".
"She's very assiduously, and in a very determined way, applying herself and the government to the issues which confront the nation - that's a good thing," he said.
TOUGH DAY FOR PM
Labor has experienced another tough day on the issue of asylum-seekers.
Earlier, Gillard said Opposition Leader Tony Abbott must commit to more than a 'narrow solution' if he is sincere about helping to put offshore processing of asylum seekers back on solid legal ground.
Mr Abbott has offered to help Labor change the Migration Act to provide legal certainty following last week's High Court ruling which sank Ms Gillard's Malaysia deal.
He's suggested the government should now look to reopen the mothballed processing centre on Nauru.
"If Mr Abbott is sincere about this offer he needs to make it very clear that he is talking about working with the government on offshore processing generally, not on his narrow solution," Ms Gillard told reporters in Canberra on Monday.
The prime minister said the opposition needed to "come to grips" with the solicitor-general's legal advice to the commonwealth.
"What that legal advice means is that we do need legislation to put beyond doubt offshore processing arrangements," she said.
"It is not correct to say based on that advice that, for example, Nauru, which is Mr Abbott's plan, could be proceeded with without legal risk."
Ms Gillard said the advice also made "crystal clear" that legislative change was needed if unaccompanied minors were to be sent overseas.
"Without that legislative change, the risk you would run is that you would send a signal to people smugglers to fill boats with children, and no one wants to see that."
The prime minister pledged the government would not adopt any new policy that breached the United Nations' refugee convention.
"Of course we wouldn't," she said.
"But there isn't one way to acquit our obligations under the refugee convention."
