Prime minister and deputy attempt to finalise details of plans to stem flow of British-born jihadis to and from Syria and Iraq

David Cameron and Nick Clegg are to hold further talks as they seek to agree on the final details of plans to stem the flow of British-born jihadis travelling to and from Syria and Iraq.

The talks on Monday come amid a warning from a former Tory solicitor general that the government needs to act within United Nations conventions.

The prime minister, who will make a statement to MPs at 3.30pm, has already reached agreement with his coalition deputy on proposals to improve the flow of information about airline passengers to intelligence agencies, and to intensify cooperation with Germany and Turkey – the main routes used by jihadis to reach Syria.

It is understood the government hopes to make it easier to stop British-born jihadis as they try to board flights from Turkey and Germany back to the UK. They would be detained for questioning if their name was "flagged" up.

Cameron and Clegg have reached broad agreement on plans to make it easier to strip suspected jihadis of their passports in Britain. But the pair will try to resolve differences on possible plans to impose a temporary ban on British-born jihadis returning to the UK, and plans to tighten up terrorism prevention and investigation measures (Tpims), the successor to control orders.

Sir Edward Garnier, the former Tory solicitor general, said the government needed to respect UN conventions and to avoid replicating existing laws.

He told the Today programme on BBC Radio 4: "We need to work out what we've got already and use those [powers]. Collect the evidence against those people who have, or may have, committed offences abroad and bring them to justice when they return.

"There are two imperatives. One is the political imperative – clearly the government has a duty to be doing things to prevent terrorists from returning to this country or doing harmful things to us in this country. That is a perfectly proper and acceptable political requirement.

"But it has to follow up those needs in a practical way and in a way which doesn't simply repeat or pass more laws which we already have. I don't complain about the government trying to get its head round this issue. What we need to be careful of in parliament is that we don't just say and do things because it sounds good when we could do those things already."

It is understood that Clegg and Cameron, who spoke on Friday before the announcement by the Joint Terrorism Analysis Centre (Jtac) that it was raising the terrorism threat level from substantial to severe, do not regard their discussions as a coalition row. They respect each other's record in speaking up on civil rights and they agree Britain must make improvements as it seeks to deal with the estimated 500 British citizens who have travelled to Syria and Iraq to fight for the Islamic State (Isis). A further 250 are believed to have returned to Britain.

Many jihadis have travelled through Germany and Turkey, which explains plans to improve cooperation with the two countries and to improve the flow of airline passenger data to the intelligence agencies. One problem is that some airlines do not release their passenger manifests until 30 minutes before flights depart.

Plans to share more passenger data will involve increasing negotiations with the European parliament, where plans to share such data have been challenged by MEPs concerned about civil liberties.

Cameron outlined plans to strengthen "information sharing" between European Union member states on airline passengers in a paper he presented to EU leaders before their summit in Brussels at the weekend. Britain wants to persuade MEPs with concerns about civil liberties to drop their opposition to an EU directive that would allow countries to collect and share passenger name records in real time.

Before the summit, a government source said: "We think there should be urgent adoption of [the directive]. It is stuck in the European parliament at the moment. It would enable much more rapid sharing and monitoring of such information."

Clegg and Cameron have a difference of opinion over plans to impose a temporary ban on returning jihadis. The discussions are focusing on the legal and practical aspects of the proposal. Legal advice has suggested that it is possible to strip a British citizen of their passport in the UK as a way of confining them to the country. But the advice also suggests that if a citizen's passport is cancelled after they have left the UK they are entitled to return home.

The pair are focusing instead on proposals that would allow authorities in the likes of Germany and Syria to prevent British-born jihadis boarding aircraft. They would then be taken in for further questioning, but would be re-admitted to Britain.

The Conservative and Liberal Democrat leaders have also yet to reach agreement on reforming Tpims after David Anderson, the independent reviewer of terrorism legislation, called for a strengthening of "locational constraints" in his annual report in March. This could ban those subject to Tpims from some areas, or restore the power to relocate them to specific areas. It is understood the discussions are focusing on how any changes to Tpims would have to make clear that these would apply only in the most exceptional circumstances.

Signs of coalition tensions were highlighted when Paddy Ashdown and Sir Menzies Campbell, two former Lib Dem leaders, criticised Cameron's response to the raising of the terrorism threat level. Cameron warned of "gaps in our armoury" as he spoke of a "generational struggle" that could see an Islamic State-led caliphate stretching to the shores of the Mediterranean.

Lord Ashdown accused Cameron of a "kneejerk" response, while Campbell warned that plans to impose a temporary ban on UK-born jihadis returning to Britain could infringe international law.

Yvette Cooper, the shadow home secretary, called for the reintroduction of tougher control orders. "Since Tpims were introduced, two terror suspects absconded – one in a black cab, one in a burqa," she said. "While the relocation power was used in control orders nobody absconded and the courts consistently upheld them as proportionate and lawful.

"There are currently no Tpims in use because the experts have warned that the police and the security services do not believe they are effective enough to be worth using."