Mr Straw told Peter Sissons on BBC TV's Breakfast with Frost that foreigners living abroad who had "no connection" with Britain should be banned from donating but government plans were "not directed at individuals".
Mr Ashcroft has said it was "appalling" that The Times newspaper had omitted a paragraph from a letter to it by David Mackilligin, Britain's former High Commissioner in Belize, backing a Tory inquiry into claims that he used his links with the previous Tory government to protect his financial interests in Belize.
The crucial paragraph said "access should not be confused with the wielding of improper influence. I never received any evidence whatsoever that there was any of the latter."
The Independent has learned that Mr Ashcroft took a group of Tory MPs to Cuba to lobby them against an American trade embargo. The revelation will irritate the US government, which uses trade sanctions against Cuba to isolate it from the West.
The Tory treasurer, a tax exile who lives in America, was thinking of buying into the island's sugar business at the time, in 1994. Then, Cuban sugar was sold mainly to the Soviet Union, but the industry suffered after the latter's collapse and the billionaire abandoned his plans.
If Mr Ashcroft had been an American he would have been barred from business with Cuba under US law, but he is a citizen of the United Kingdom, Belize and the Turks and Caicos.
Mr Ashcroft, whose main home is in Florida, took the four MPs - Sir Tom Arnold, Jacques Arnold, Andrew Rowe and Richard Tracey - to Cuba, Panama and the Turks and Caicos. Sir Tom left and the other MPs went on to Belize.
Mr Rowe, member for Faversham and Mid-Kent and the only one still an MP, said the trip changed his view of the American trade embargo. "We talked to Cubans and it became perfectly clear that if the Americans lifted the sanctions the vast majority of people would much prefer to do trade with the US," he said.
Jacques Arnold, who lost his Gravesham seat in 1997, said he had an interest in Latin America. Mr Ashcroft had showed the MPs a rice mill on Grand Turk and an orange-juice processing plant in Belize, Mr Arnold said. He was hoping to set up a project in Cuba, possibly growing and processing sugar cane.
Review, page 4