He told the BBC there was no basis for any military action despite suspicions over Iran’s nuclear programme.
US press reports say Washington is drawing up plans for attacks on Iran’s nuclear sites. One article suggests the possibility of a nuclear strike.
Iran has said the reports are no more than a form of “psychological warfare”.
The UN’s top nuclear inspector Mohamed ElBaradei is to visit Iran this week, amid growing international pressure on Tehran to end the enrichment of uranium, which it restarted in January.
In the BBC interview, Mr Straw was responding to a report by Seymour Hersh in the New Yorker magazine that the Pentagon was stepping up plans for a possible air strike on Iranian nuclear facilities.
The Washington Post has also reported that the US may be considering military action, although it said no attack was likely in the short term.
The paper said the US wants to show Iran it is ready to use force if necessary.
But Mr Straw told BBC One’s Sunday AM show there was “no smoking gun” to justify an attack on Iran despite “high suspicion” over its nuclear work.
“We can’t be certain about Iran’s intentions and that is therefore not a basis for which anybody would gain authority to go to military action,” he said.
Iran’s foreign ministry dismissed the US media reports as a form of intimidation “stemming from America’s anger and helplessness”.
UN inspections
Mr ElBaradei, who heads the International Atomic Energy Agency (IAEA), will be joining a team of five UN inspectors that is already in Iran.
Iranian television on Sunday showed UN inspectors examining a nuclear facility at Isfahan, and said they had earlier visited the uranium enrichment plant at Natanz.
“The mere existence of the inspectors in Iran shows our serious co-operation with the IAEA,” said an Iranian foreign ministry spokesman, Hamid Reza Asefi.
The UN Security Council has given Iran 30 days to halt its nuclear research, or run the risk of action such as possible sanctions.
The deadline was imposed on 29 March, and so far Iran has insisted its work will go on.
Mr ElBaradei is expected to report back to the UN Security Council on Iran’s response to its demands.
