The political pressure on David Cameron to explain Britain’s role in a potential “stabilisation force” in Libya has increased as he was pressed to give evidence to the foreign affairs select committee on the UK’s strategy.

The committee is conducting an inquiry into British planning for Libya in the wake of the downfall of its dictator, Muammar Gaddafi, in 2011, as well as into how to end the political and security chaos that has gripped the country since.

Concerns are growing that Islamic State is building a stronghold in parts of the country, and that by the summer the European Union could face another wave of refugees from north Africa.

There has been widespread discussion of an intervention in which Britain would provide 1,000 non-combat troops to a 5,000-strong force to train and advise the Libyan army to help it become capable of driving out Isis.

On Thursday, as the British defence secretary, Michael Fallon, met his Italian counterpart in London to go through the details of their potential joint role, the committee’s chairman, Crispin Blunt, asked Cameron to give evidence in a bid to flush out Whitehall thinking.

Prime ministers by tradition tend not to give evidence to departmental select committees. But Cameron may feel required to make an exception given the likelihood of him being severely criticised by the inquiry for failing to plan for the post-intervention aftermath in Libya in a similar way to the failure in Iraq.

The inquiry has been given an added geopolitical relevance by the recent claim by the US president, Barack Obama, in a magazine interview that Cameron had become “distracted by a range of other things” after the Libyan intervention, and was in part responsible for the “mess”.

David Cameron was distracted during Libya crisis, says Barack Obama Read more

Cameron has blamed Libyan politicians for failing to seize the chance for democracy that predominantly French and British forces provided by undermining Gaddafi.

Blunt, in his letter, says the request to give evidence has been sent in the spirit of fairness and genuine inquiry. The report is likely to be highly sceptical of what role the UK can play in a stabilisation force if British forces are confined to training a nascent Libyan national army.

It is thought UK special forces, as well as ariel intelligence, are already operating in Libya, and the UK has also allowed US air forces based in Lakenheath to hit Isis targets in the country.

On Wednesday, at prime minister’s questions, Cameron hinted he would allow a Commons vote if UK forces were to be sent to the region, but it may be argued that the forces will not be involved in combat and so do not need the formal approval of parliament.

“If we had any plans to send conventional forces for training in Libya we would of course come to this house and discuss them,” he said. “What we want to see in Libya is the formation of a unity government.”

It has been agreed that there will be no international intervention without a formal invitation from the newly formed Libyan government of national accord.

The French foreign minister, Jean-Marc Ayrault, will meet the Libyan prime minister-designate, Fayez Seraj, on Friday to discuss the terms of that invitation. After months of delay, the Libyan unity government has been formed, but it is yet to move from Tunis to Tripoli, the capital and natural centre of government.

The Italians believe no further UN security council resolution is needed so long as the invitation comes from the internationally recognised government of Libya.

The Egyptian president, Abdel Fatah al-Sisi, has warned western powers Libya could spiral out of control if they try to intervene militarily.

Speaking in a rare interview, the military-backed ruler of one of the region’s biggest powers said the west and its allies should instead concentrate on strengthening the army of Libya’s internationally recognised government and let it do the job of stabilising the country.

“If we provide arms and support to the national Libyan army it can do the job better than anyone else, better than any outside intervention which would risk dragging us into a situation that risks getting out of hand and triggering uncontrollable developments,” Sisi told Italy’s La Repubblica in an interview.

Sisi said history had “spoken clearly” about the difficulty of trying to impose peace from outside. “Two lessons must be kept in mind: that of Afghanistan and that of Somalia,” he said. “Those were long foreign interventions (that started) more than 30 years ago and what progress has been made since? The results are there for everyone to see.”

Sisi also suggested that European governments were underestimating the scale of Islamist influence in Libya. “Europeans look at Libya as if Isis was the only threat,” he said. “That is a serious mistake. We have to be aware that we are up against different acronyms with the same ideology: what do we say about al-Qaida networks like Ansar al-Islam, like Somalia’s al-Shabaab or Boko Haram in Africa.”