An investigation by the Observer newspaper claims that the minister was phoned by Iraqi-born entrepreneur Nadhmi Auchi for advice on how to avoid extradition from the UK.
Conservative party chairman Michael Ancram says Tony Blair should sack the minister if he refuses to immediately explain his actions.
A Labour party spokesman confirmed Mr Vaz had contacted the Home Office and passed the findings onto Mr Auchi's owm constituency MP - none of which was either illegal or improper.
Mr Ancram said: "These latest revelations concerning the Minister for Sleaze Keith Vaz are devastating.
"It is simply unacceptable for Mr Blair and Mr Vaz to say that nothing will be done until after the election."
He said the prime minister must insist on Mr Vaz explaining his actions as soon as possible.
"The only alternative is for Mr Blair to sack Mr Vaz as a minister," he argued.
Mr Auchi, who owns a banking and construction group, is wanted by French police on a number of charges including receiving embezzled company assets.
But the businessman denies any wrongdoing.
The Observer says that Mr Vaz, who was a director of Mr Auchi's corporation before he became a minister, was phoned by the businessman for advice on how to avoid extradition from the UK.
A Labour party spokesman said the minister had made a factual inquiry to the Home Office on Mr Auchi's behalf as any MP was entitled to do.
This was then passed to Mr Auchi's own constituency MP.
Mr Vaz has been on sick leave since March after coming under intense media pressure over his business interests.
A parliamentary inquiry found him guilty of failing to declare a payment from a local solicitor but cleared him of nine other charges.
No conclusions were reached on another eight because of a lack of evidence.
Mr Vaz is still facing a separate investigation into alleged links between the wealthy Hinduja Brothers and a company run by his wife.
In recent weeks he has been campaigning in his Leicester constituency.