Health Secretary Vaughan Gething told a BBC Radio Wales election phone-in he had not backed Mr Corbyn in the last two leadership contests, but still wanted him to become prime minister.
"I don't think it matters whether I'm a fan or not," he said.
"The alternative is the Tories able to do what exactly they want."
Speaking on the Jason Mohammad programme, Mr Gething rejected listeners' suggestions that Welsh Labour was failing to support the party's UK leader.
"I want a Labour prime minister - and that means Jeremy Corbyn being prime minister," he said.
"I don't think it matters whether I'm a fan or not - it matters whether I think he can do the job in running the country.
"It matters whether I think this country will be better off having a Labour prime minister than a Tory."
Mr Gething admitted he had not backed Mr Corbyn in the last two Labour leadership contests, but accepted the party had voted "decisively" for him to be its leader and candidate for prime minister.
He said he also wanted to see Welsh Labour MPs "being returned from Wales in large numbers".
"We know the alternative is the Tories able to do what exactly they want, so it's up to us to stand up for Wales," he said.
Mr Gething dismissed the idea that Labour was under threat in Wales from the Conservatives and Plaid Cymru.
"I don't think we will be wiped out here," he said.
"We've got a good record in government ... we're directly engaged in our local communities," he added, pointing to the fact that Labour held onto control of seven councils after the local elections in May.
Questioned about policy issues, Mr Gething said Labour was "appalled" that the Conservatives were planning to abandon the "triple lock" guarantee on pensions, and claimed working people were worse off under the Tories.
On Europe, he said Labour would argue for a "more open relationship" with the EU than a "hard" Brexit, calling for "full and unfettered" access to the single market and freedom of movement to work.
Mr Gething said he recognised public concern about immigration, but insisted that most migration was "economically beneficial".
"There's a challenge for us about understanding what sort of deal we can have with Europe that doesn't compromise Welsh jobs and investment," he said.
"I do not think that people voted to make themselves poorer, but that is exactly what I think a hard Brexit would do, and that's what Theresa May wants."
Welsh Conservative leader Andrew RT Davies responded: "A vote for Labour is a vote for more debt, more taxation and a chaotic Brexit, no matter how cynically Welsh Labour ministers attempt to carve out a distinct brand for themselves."
Labour figures in Wales are not trying to distance themselves from party leader Jeremy Corbyn, a Welsh Government minister has insisted.