"It looks from the way in which the national results are going that Mr Blair is going to win a third term for Labour," Howard said in a speech following his own re-election as member of parliament for Folkestone, in southern England.
Blair's party secured a historic third term in office, having won 353 parliamentary seats decided so far in Thursday's general elections.
Labour needed 324 of the 646 seats up for grabs to win a simple majority.
The opposition Conservatives and the Liberal Democrats picked up 196 and 61 seats respectively. Smaller parties or independents won 12 seats.
Blair addressed reporters shortly after returning from Buckingham Palace, where Queen Elizabeth II confirmed him as prime minister for a third term.
"It's a tremendous honour and a privilege to be elected for a third term. And I'm acutely conscious of that honour and that privilege," Blair said, speaking outside his Downing Street office.
"I know that Iraq has been a deeply divisive issue in this country... But I also know and believe that after this election, people want to move on, they want to focus on the future - in Iraq, and here," added Blair.