The West has heaped pressure on rival Libyan politicians to form a unity government as the need for a stable ally to take on Islamic State (ISIS) group militants in the country grows ever more pressing.

The UN hopes that a recent agreement signed between rival Libyan politicians will help end the chaos and conflict that has gripped the country since the fall of dictator Moamer Ghaddafi in 2011.

But the deal does not have the full support of both of the country's rival parliaments and the UN itself has called it a "first step".

The disorder has provided fertile ground for jihadists and people-smugglers to flourish, and the growing strength of ISIS in Libya has alarmed the West, which finds itself without a stable partner to work with against the radical group.

With a unity government in place, "we can imagine that a call to help will one day be directed to the West" to fight ISIS, said Marc Pierini, an analyst with the Carnegie centre and European Union ambassador to Tripoli.

"But the road is still long because this hard-won deal is very fragile," he told AFP.

The deal was signed by less than half of the members of Libya's internationally recognised parliament based in eastern Tobruk, and about a third of the members of the rival parliament based in Tripoli.

And the heads of both assemblies have outright rejected it, with critics saying it risks creating a third government in Libya and further deepening divisions.

Adding to the confusion, members of the two bodies launched an alternative peace process in Tunis on December 6 that has been backed by the two parliament heads.

"There are a large number of people fighting on the ground who are not signatories" of the accord," said Shashank Joshi of the Royal United Services Institute (RUSI) in London.

"The agreement is very fragile."

Western nations, already battling ISIS in Iraq and Syria and desperate to prevent its spread elsewhere, have welcomed the deal despite the potential pitfalls.

A single and stable government would provide the West with a legitimate ally in Libya and offers of assistance to such a government have been pouring in.

"This agreement means the international community can now engage with one unified, representative government in Libya in the fight against Daesh (ISIS) and the migrant traffickers," said British Prime Minister David Cameron last week.

Rome has repeatedly stated its willingness to lead a peacekeeping force on the ground should it get the green light from a national unity government and get the UN to sign off.

The French army in November carried out reconnaissance flights above Sirte, the Libyan stronghold of IS, where a French source said the jihadists have some 3,000 fighters.

"We are at war, we have an enemy, Daesh, that we must fight and crush, in Syria, in Iraq and tomorrow without doubt in Libya," French Prime Minister Manuel Valls said earlier this month.

NATO chief Jens Stoltenberg has said the alliance will "provide assistance" to a national unity government, but opposes any new military intervention in Libya.

The US is "committed to providing the unified government full political backing and technical, economic, security, and counterterrorism assistance," said State Department spokesman John Kirby.

The United States has been quietly targeting IS in the country, claiming to have killed its Libyan leader, Abu Nabil, with a drone strike on a compound in Derna on November 13.

It has also sent a group of special operations troops to Libya to "foster relationships" but they were kicked out of the conflict-torn country soon after they arrived.