Labour Leader Ed Miliband is to urge for parliament to sit for an extra day on Wednesday to discuss the phone hacking crisis.
In a speech on Monday he is expected to say that extending the parliamentary session would be the "right and responsible thing for the government to do".
"Rebekah Brooks has been arrested, the Metropolitan police commissioner has resigned, tomorrow we will have some of the most important select committee hearings in modern times and the prime minister has decided to leave the country, not to return until after parliament breaks up for summer," he said.
"In these circumstances the right and responsible thing for the government to do must be to extend the parliamentary session for at least 24 hours so the House of Commons meets on Wednesday.
"It would give MPs have the chance to debate the issues arising from the select committee hearings and ensure the prime minister answers the many unanswered questions that he faces.
"Unless the government agrees to parliament meeting on Wednesday, MPs cannot do their jobs properly and the prime minister has no chance of sorting out this crisis."
The Commons culture select committee will question Rebekah Brooks, former News International chief executive, along with Rupert Murdoch, the News Corp chairman, and his son James, who looks after the company's Asia and Europe interests, at a hearing on Tuesday.
Brooks was arrested on Sunday night but a spokesman said she still intended to appear before the committee, the BBC's Robert Peston reported.
Prime Minister David Cameron responded to Miliband's call saying that "it may well be right" for parliament to sit for an extra day after recess on Wednesday.
Speaking from Johannesburg, where he met with South African President Jacob Zuma to discuss trade and the situation in Libya, Cameron defended the work former-News of the World editor Andy Coulson while in office as Number 10 press chief.
Cameron said: "The situation in the Metropolitan police service is quite different to the situation in government, not least as the issues that have emerged and the Met are looking at have a direct bearing on the police inquiry."
Defending his decision to travel to Africa amid the phone hacking crisis and the Cameron said the prime minister had a duty to promote British trade.
"I think it is right for Britain to be engaged with South Africa and Africa as a whole," Cameron said. "There is a huge opportunity for trade, growth, jobs including jobs at home in the UK and I think it is right for the British prime minister to be out there with British businesses."
He added that he was still in constant contact with his staff in the UK. "Just because you're travelling to Africa doesn't mean you suddenly lose contact with your office," he said. "The government is pressing ahead on all of the fronts that I set out in my statement last week."