David Cameron has said the Commons will be recalled on Wednesday to debate the latest developments in the phone hacking scandal.
MPs were due to begin a six-week recess at the end of Tuesday.
But Labour have demanded an extra day's sitting to enable MPs to consider what is said by Rupert Murdoch and Sir Paul Stephenson at committees on Tuesday.
The PM said it would be "right" to make a statement on Wednesday and answer questions "arising" from the hearings.
In other developments on Monday:
The Metropolitan Police Authority's professional standards committee is to make a statement about the future of Assistant Commissioner John Yates amid growing calls for him to quit
Former News International chief executive Rebekah Brooks confirms she will appear before a committee of MPs on Tuesday despite her arrest and questioning by police
The Serious Fraud Office says it will give "full consideration" to a request by Labour MP Tom Watson to investigate out-of-court settlements made to hacking victims
Shares in News Corporation drop by 7.6% to a two-year low in trading in Australia.
Pressure has been growing on the Commons to keep sitting on Wednesday as the scandal surrounding News International and the police continues to intensify.
Rupert Murdoch, his son James and former News International chief executive Rebekah Brooks are set to face questions on Tuesday afternoon from the Commons culture committee over what went on at the News of The World and what they knew about it.
Earlier on Tuesday, Met Commissioner Sir Paul Stephenson - who announced his resignation on Sunday amid allegations about the force's relationship with former News of the World deputy editor Neil Wallis - is due to appear before the home affairs select committee.
Speaking in South Africa, where he is on a trade trip, Mr Cameron said he believed it would be appropriate for MPs to sit an extra day to discuss these developments.
It is up to the Commons Speaker John Bercow to decide whether to extend the Commons sitting.
Downing Street said they expected the prime minister to make a statement and take questions from MPs afterwards but Labour leader Ed Miliband called for a full debate - but prime minister's questions, which is normally held on a Wednesday, would not be taking place.
"We must give MPs the chance to debate the issues arising from the select committee hearing and ensure the prime minister addresses the many unanswered questions that he faces," he said.
'Fleeing the country'
Mr Cameron has faced criticism for the timing of his trip to Africa, one Conservative backbencher telling BBC News it appeared the PM was "fleeing the country".
But the prime minister defended his decision saying: "It is important for the prime minister to get out there with British business at a time when we need investment and growth and jobs back at home."
And he said he had been in touch with Home Secretary Theresa May and other key figures to discuss the latest developments.
"Just because you are travelling to Africa does not mean you suddenly lose contact with your office," he added.
Mr Cameron was also quizzed about Sir Paul Stephenson's resignation - and the reference in his resignation statement to the prime minister's close relationship with the News of the World's former editor, Andy Coulson.
He rejected suggestions that there was any similarity between Neil Wallis being employed by Scotland Yard and Mr Coulson working in Downing Street.
"The situation in the Metropolitan Police Service is really quite different to the situation in the government, not least because the issues that the Metropolitan Police are looking at, the issues around them, have had a direct bearing on public confidence into the police inquiry into the News of the World and indeed into the police themselves."
But Labour said the prime minister was "hamstrung" from dealing with the crisis of confidence in the media and the police because of his decision to employ Mr Coulson.
"It is also striking that Sir Paul Stephenson has taken responsibility and resigned over the employment of Mr Coulson's deputy, while the prime minister has not even apologised for hiring Mr Coulson," said Labour leader Ed Miliband.
Yates future
Home Secretary Theresa May is due to update MPs on Sir Paul's resignation later on Monday.
At the same time, the Metropolitan Police Authority is expected to make a statement about the future of Assistant Commissioner John Yates following a meeting of its professional standards committee.
Mr Yates, who has been asked to attend Tuesday's Home Affairs committee meeting, is facing calls for him to consider his position after being widely criticised for deciding not to reopen the Met's hacking inquiry following a review of new evidence in 2009.
The BBC's Political Editor Nick Robinson said Mr Yates had also been in charge of checking out Mr Wallis, before he was given a contract to provide communications advice by the Metropolitan Police.
He said Mr Yates was given categorical assurances from Wallis that nothing would emerge that would embarrass either of them or the Met Commissioner.
