Tessa Jowell has joined a series of senior ministers in calling for Gordon Brown to be elected unopposed as the next Labour Party leader.
The culture secretary said on Sunday that the chancellor would take over as prime minister by the end of the parliament.
And she argued that the inevitability of the outcome would only make any internal contest damaging.
"I believe that Gordon Brown will succeed Tony Blair as prime minister when the time comes," she told GMTV's Sunday programme.
"I don't think that a contest for the sake of a contest is necessarily healthy. I think there is a pretty settled consensus in the country.
"I think there is a pretty settled consensus in the government because of the consensus in the country about the direction of travel. So I think fabricating a contest for the sake of a contest would frankly be a waste of time and a waste of energy."
Other Cabinet members including Charles Clarke, David Miliband and Patricia Hewitt have all rallied behind Brown in recent days ahead of the party's annual conference in Brighton this week.
However some figures on the left of Labour, including former environment minister Michael Meacher, have said the party should have a contest in order to debate its future direction.
And defence secretary John Reid refused to endorse Brown in an interview on Sky News on Sunday.
Succession
Blair himself also refused to comment on the speculation in his own pre-conference interview on Sunday.
"I have said all I have got to say on this and this week should be about setting out an agenda for the country," he told the BBC.
However he conspicuously failed to commit again to serving a "full third term".
But Jowell said the prime minister would continue in Number 10 for the whole parliament.
"The next election will be round about 2009," she said.
"It doesn't have to be until 2010 but no, he has been very clear that he will serve a full third term."
Meanwhile former deputy Labour leader Lord Hattersley said Blair was now a "dead duck".
"I think the pressures on him will make life impossible. Every day that passes he's more and more of a dead duck," the peer said.
"I think his goodwill begins to run out with every week and month that passes. And he can't go to a party conference two years, three years from now still as prime minister.
"I wouldn't put it past him if he could get away with it but I don't think he can get away with it."
