Theresa May was told about a recent Trident test happening when she became PM, Downing Street has said, amid reports a missile went off course.
Labour and the SNP are urging the government to explain whether a test firing from HMS Vengeance went wrong.
The incident reportedly happened a few weeks before MPs voted to renew the UK’s nuclear weapons system.
Defence Secretary Sir Michael Fallon told MPs he had “absolute confidence” in Trident.
The Ministry of Defence says submarine HMS Vengeance and its crew were “successfully tested” last June.
But shadow chancellor John McDonnell said it was “extremely worrying” Parliament had not been told of the incident when voting on renewing Trident in July.
Meanwhile, Scottish First Minister Nicola Sturgeon, a long-standing opponent of Trident, whose submarines are based at Faslane, on the River Clyde, called the apparent misfire a “hugely serious issue”.
BBC defence correspondent Jonathan Beale says the Royal Navy has carried out half a dozen such tests since 2000 and in the past has publicised successful launches, but this time did not.
It’s one of the simplest questions in politics, and one of the most troublesome.
At the start of a critical political week, Theresa May finds herself under pressure for refusing to answer it.
Did she, or did she not know that something had gone wrong with our nuclear weapons, when she asked MPs to vote to renew the costly Trident system?
HMS Vengeance, one of the UK’s four Vanguard-class submarines, returned to sea for trials in December 2015 after a £350m refit, which included the installation of new missile launch equipment and upgraded computer systems.
According to the Sunday Times, the unarmed Trident II D5 missile was intended to be fired 5,600 miles (9,012 km) from the coast of Florida to a sea target off the west coast of Africa – but veered towards the US.
In July, days after Mrs May had become prime minister following David Cameron’s resignation, MPs backed the £40bn renewal of Trident by 472 votes to 117.
During the debate, Mrs May told MPs it would be “an act of gross irresponsibility” for the UK to abandon its nuclear weapons.
But 52 SNP MPs voted against it, as did 47 Labour MPs, including party leader Jeremy Corbyn.
A Downing Street spokeswoman said Mrs May had been briefed on a range of nuclear issues, including the test, when she became prime minister.
Asked whether a missile had mis-fired, she said she was not going to get into “operational details” and would not say whether Mrs May had been told this.
Questioned by the BBC’s Andrew Marr on Sunday, Prime Minister Theresa May refused four times to say whether she had known about the test firing ahead of the vote.
Mrs May said: “I have absolute faith in our Trident missiles. When I made that speech in the House of Commons, what we were talking about was whether or not we should renew our Trident.”
What is Trident?
The Trident system was acquired by the Thatcher government in the early 1980s as a replacement for the Polaris missile system, which the UK had possessed since the 1960s.
Trident came into use in the 1990s. There are three parts to it – submarines, missiles and warheads. Although each component has years of use left, they cannot last indefinitely.
The current generation of four submarines would begin to end their working lives some time in the late 2020s.
Labour leader Jeremy Corbyn said the reports called for “a serious discussion”. He told Sky News: “It’s a pretty catastrophic error when a missile goes in the wrong direction.”
Shadow defence secretary Nia Griffith told BBC Radio 4’s Today programme that she wanted a “clear and honest picture” from Mrs May.
“Of course we are not asking for any inappropriate detail to be revealed,” she said. “But we are asking what happened and what the MoD has done since to make sure that things have been put right,” she said.
‘Bizarre and stupid’
Conservative MP Julian Lewis, chairman of the Commons Defence Committee, said Mrs May had been “handed a no-win situation” by her predecessor as Prime Minister, David Cameron, whose “spin doctors” had been responsible for a “cover-up”.
He told Today that the government usually released film footage of the “99%” of missile tests deemed a success and that ministers could not “have it both ways” by not announcing when this had not been the case.
But a spokesman for Mr Cameron said: “It is entirely false to suggest that David Cameron’s media team covered up or suggested a cover-up for the Trident missile test.
“We were disappointed Julian Lewis would make these claims without any evidence.”
Mr Lewis later told the BBC’s Daily Politics that if Sir Craig Oliver (David Cameron’s former communications director) “didn’t know, did the [then] Prime Minister know? And if the Prime Minister knew, why didn’t he make the matter public and why didn’t he tell even his closest spin doctors?”
Caroline Lucas, co-leader of the Green Party of England and Wales, called for “full disclosure”, adding: “A missile veering off course is deeply concerning. Imagine such a failure occurring in a ‘real-world’ situation – it could lead to the slaughter of millions of people in an ally’s country.”
Kate Hudson, general secretary of the Campaign for Nuclear Disarmament, said: “There’s absolutely no doubt that this would have impacted on the debate in Parliament.”
But former nuclear submarine commander and Ulster Unionist Party assembly member, Steve Aiken, told Today that any fault “would have been sorted out”.
“There is a convention that we don’t talk about the deterrent… because that is the nature of the deterrent – it is about the security of this nation and I would fully support the prime minister in avoiding those questions,” he said.
A statement issued by Downing Street and the MoD said the capability and effectiveness of Trident was “unquestionable”.
“In June the Royal Navy conducted a routine, unarmed Trident missile test launch from HMS Vengeance, as part of an operation which is designed to certify the submarine and its crew.
“Vengeance and her crew were successfully tested and certified, allowing Vengeance to return into service. We have absolute confidence in our independent nuclear deterrent.”