The British government is facing new pressure to publish any plans it has for troop deployments to Libya after it was disclosed that five separate international security operations are being considered for the war-torn country.

EU ministers meet on Monday to discuss sending security units to Tripoli. Other missions in the works include bombing Islamic State fighters, training Libyan troops, combating people smugglers and disarming militias. Most are likely to involve British personnel.

Senior MPs are demanding a statement on what part British forces will play, after foreign secretary Philip Hammond insisted last week that no decisions had been made on any operations.

“Clarity is now overdue. We need transparency about the difficulties and the challenges,” Crispin Blunt, chairman of parliament’s foreign affairs committee, told the Observer. “Any deployment would need a parliamentary vote, as would airstrikes on Isis.”

Planning for the missions is taking place amid anxiety that Libya is crumbling, and that the newly installed Libyan government cannot combat the rise of Isis and migrant smuggling without foreign help. A draft of Monday night’s EU closing statement, leaked to Reuters, says the EU “stands ready to offer security sector support” to Libya, probably including police and non-military advisers. EU foreign policy chief Federica Mogherini said the meeting would discuss “the way forward to the different security assets we have, especially connected to the Sahel and Libya”.

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While the EU operation is limited to police units, up to 1,000 British troops may be deployed in a parallel Libya International Assistance Mission, or Liam, led by Italy and tasked with training a new army. Separately, last month it was disclosed that SAS units are already in the country, working alongside American special forces to identify Isis targets for airstrikes. Meanwhile EU naval assets, including Royal Navy survey ship HMS Enterprise, are planning an escalation, backed by David Cameron, of an operation – called Sophia – against migrant smugglers, moving it inshore to intercept craft as they leave the Libyan coast. And Nato secretary general Jens Stoltenberg last week disclosed willingness to send units to disarm the country’s militias.

Diplomats caution that missions will go ahead only if requested by Libya’s new “government of national accord”, which is struggling to assert itself. But America’s Libya envoy, Jonathan Winer, tweeted on Friday that time was short: “#ISIL #DAESH threat to #Libya @ its people real – #LGNA must decide how to use intl offers to help.”

Washington has not offered troops; it insists that Europe take the lead in fixing Libya’s post-conflict problems. Last week Barack Obama said US failure to support Libya after its 2011 Arab spring revolution was the worst mistake of his presidency. In London, MPs remain at loggerheads with the government over its refusal to make military plans public. Downing Street is worried about a rerun of last year’s contentious parliamentary debate about airstrikes on Isis in Syria. Last week, Hammond exchanged testy letters with Blunt, in which he denied claims that the committee was briefed by diplomats on the Liam plan. Blunt in turn accused Hammond of being “deliberately misleading”, saying details of Liam were given by a UK official at Britain’s embassy in Tunis. “The operation we were briefed on involved setting up shop at Tripoli airport or the port where the coastguard are,” said Blunt.

He said MPs were concerned that the different military options for Libya lack coordination. “In cases like this, where things are difficult, you need a proper policy objective. What are you trying to do? If all you’re doing is opening up a new set of complexities and unknowns, it may be an idea not to do it.”

Britain insists that the new government is making progress, with ambassador Peter Millet joining French and Spanish counterparts in Libya’s capital last week in their first visit since western embassies were evacuated in 2014.

A Foreign Office spokesperson said: “The UK continues to work with international partners on how to best support the new Libyan government. This includes discussions about a Libyan International Assistance Mission. It is up to the new Libyan government to tell us what sort of help they want.”

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A Libyan request for support may come on Monday, when the newly installed prime minister, Fayez al-Sarraj, is due to speak to EU ministers in Luxembourg by video link.

MPs also want to quiz Hammond on his decision to back the new government and rely on it to channel any military assistance. Sarraj, an affable 56-year-old from Tripoli, is popular with diplomats, who regard him as a neutral figure not aligned to any of Libya’s myriad armed factions. But his nine-member government has not been elected. Instead, it derives its authority from a UN-chaired negotiation committee, which leaves many Libyans questioning its legitimacy.

“The GNA, even if it is supported by the international community and UN security council, is based on an ambiguous and unclear political agreement,” says Libyan activist Hana Gallal. “It is singling out certain players and ignoring the rest.”

Three weeks after arriving in Tripoli, Sarraj is stuck in the city’s naval base, opposed by Libya’s two existing governments, in Tripoli and Tobruk, who are also at war with each other. In Tripoli, the Islamist-led National Salvation government is refusing to cede power, leaving the city divided, with militias loyal to Serraj in eastern and central districts and rival militias elsewhere. Aguila Saleh, president of the Tobruk parliament, has accused UN envoy Martin Kobler of acting like a governor not a mediator in urging support for the Sarraj government.

International officials fear that if military intervention is delayed, Isis will grow stronger in the region, launching repeats of last summer’s attacks in which 38 tourists, 30 of them British, were killed in Tunisia’s Sousse resort.

“The fear is that the summer will create better conditions for Islamic State to carry out cross-border attacks,” said US analyst Geoff Porter. Taking advantage of the chaos, Isis last week continued attacks in the oil-rich Sirte basin, with half a dozen oilfields hurriedly evacuated.

Migration from Libya to Europe is meanwhile surging, after the closure of the popular route from Turkey to Greece. Two thousand people a day, mostly from sub-Saharan Africa, now make the dangerous crossing from Libya to Italy and the International Office of Migration is warning that many hundreds of thousands may follow.