Mr Straw said it was "imperative" that Mr Nadir return to Britain to face the "serious fraud offences" of which he was accused.
That was the way Mr Nadir - who allegedly jumped bail four years ago and fled to northern Cyprus - should seek to clear his name if he believed he had the evidence to do so, said Mr Straw.
"He has nothing to fear from British justice."
The Home Secretary was responding to remarks by Mr Nadir that he would consider returning to this country providing the Prime Minister promised he would not be arrested.
Mr Nadir also demanded a public inquiry into allegations surrounding his collapsed Polly Peck empire. He fled to Cyprus in 1993 when his business became the centre of a Serious Fraud Office investigation.
Charges were brought against him but he never went to trial, leaving the allegations outstanding.
Mr Nadir told BBC Radio 4's Today programme: "I will be asking again, like numerous people have asked in Britain during the years I was there, that the new British government now will be sufficiently brave to clear this matter.
"And the request that I will be putting in again today is that Mr Blair can ask whether he is going to have a public inquiry.
"I cannot emphasise strongly enough the relevance of a public inquiry."
He added: "If I have an assurance to the government of Turkey that I will not be arrested, if I could have a guarantee government to government, I would be delighted to come back with a definite undertaking that there will be a public inquiry."
Pressed on why he had not stayed in Britain to face the charges, Mr Nadir suggested there had been impropriety in the way the matter was handled, and claimed there had been a "conspiracy".
Mr Nadir later told a news conference in Istanbul that he was preparing to take Britain to court over the collapse of his Polly Peck empire.
"Cases are ready against the British government and its various organs that have committed crimes," he said.