Just three days after getting the job she was thrown in at the diplomatic deep end, heading to New York for her first meeting with her US counterpart Condoleezza Rice and discussions with other foreign ministers aimed at finding a common approach towards Tehran.
Mrs Beckett said she, the American Secretary of State and their colleagues from France, Germany, Russia and China had not discussed the text of a proposed resolution demanding Iran ends its uranium enrichment work - a key step in developing a nuclear bomb.
But she said they were all agreed that no-one wanted Iran to have nuclear weapons and that it should stop enrichment work.
Officials had a "good deal of work" to do when they come back to the negotiating table this morning to try to reach an agreement on a resolution, against the background of "clear common ground" on objectives, she added.
Asked whether she believed a military strike on Iran was inconceivable - the word used repeatedly by Mr Straw - Mrs Beckett said: "No-one has the intention to take military action.
"That was not discussed, it's not an issue.
"What people are concerned to do is to get Iran to recognise the strong view and the clear will of the international community that they should comply with the IEAE (International Atomic Energy Agency) board."
She added: "You're inviting me to tread down the path of talking about military action - I'm not going to do that.
"Everybody expresses their views, their stance, in their own way. The way that I choose to express it is that it's not anybody's intention to take the course of military action.
"That I think is simple and straightforward and clear."
Yesterday, Prime Minister Tony Blair dismissed as "utterly absurd" claims that Mr Straw had been sacked as Foreign Secretary because of his unequivocal policy on Iran.
Mr Blair said he had no doubt that foreign policy would "not change one iota" under Mrs Beckett.
French Foreign Minister Philippe Douste-Blazy said the late-night meeting over dinner at the Waldorf Astoria hotel had failed to reach agreement on how to deal with Tehran.
He told reporters afterwards: "We are still considering our work."
The US dismissed a letter from Iran's leader, President Mahmoud Ahmadinejad, saying it proposed nothing new.
Britain and France, backed by the US, have proposed a formal Security Council resolution demanding that Tehran suspend uranium enrichment, and insist it must be under Chapter 7 of the UN Charter to make it legally binding.
But Russia and China are wary, fearing it could lead to a re-run of the Iraq crisis.
"The discussions we have had this evening, we have not - and this was said explicitly from the beginning - we have not been negotiating texts, we have been discussing basic issues, the background strategy," Mrs Beckett said.
She added that sanctions might be needed to make Iran comply.
"No one wants to apply sanctions if it's not necessary but what everybody wants is to get Iran to recognise that the international community is serious in its insistence that we cannot continue with the assumption that Iran can just continue to flout the will of the international community this way," she said.
Mrs Beckett paid tribute to Mr Straw, saying he had done a "huge amount of detailed and skilled work" on the issue.
"It's my first full day tackling what is a hugely important and difficult issue, which I suppose is characteristic for this portfolio," she said.
Earlier, Mrs Beckett and Dr Rice, who represent the first all-female US-UK foreign minister pairing, got together on their own for the first time to get to know each other.
They chatted about their backgrounds and how they got to their respective positions in a "wonderful discussion", Dr Rice said. Mrs Beckett told the Secretary of State she had heard so much about her from Mr Straw - with whom Dr Rice had a famously close working relationship - that she felt she knew her already.
"There is a very strong relationship between our two countries and I feel confident that we will have a good working relationship," Mrs Beckett said.
Dr Rice added: "We look forward to talking about the many challenges that we have."
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