The formation of a unity government in Libya has been dealt a blow with the rejection on Monday of the 32-member cabinet proposed by the country's new Government of National Accord.

The cabinet was rejected by the Tobruk-based House of Representatives (HOR), Libya's internationally recognised parliament. The nine-member presidential council that heads the Government of National Accord, or GNA, nominated the cabinet last week.

The new government is intended to replace two administrations that have been competing for control of Libya since mid-2014: the internationally recognised government based in Tobruk in the northeast, and the unofficial Government of National Salvation based in Tripoli.

The HOR demanded the reduction of the cabinet to 17 members, and rejected the proposed removal of Khalifa Haftar, the head of the Libyan National Army, a group of militias affiliated to the eastern government.

The creation of the GNA was mandated last month in a compromise agreement between representatives of the rival administrations and other political stakeholders - the culmination of a year-long process of UN-sponsored negotiations. The presidential council was given a month to agree on a list of personalities to form the new government, and it completed the task two days after the scheduled deadline.

Ending the situation of parallel governments - each with its own parliament and a host of militias fighting on its behalf - is critical to Libya's future stability and prosperity.

READ MORE: Libya - A tale of two governments

Clashes between the two administrations have prevented a co-ordinated approach to the marketing of oil, contributing substantially to a drop in oil production to fewer than 400,000 barrels a day (b/d) from 1.6 million b/d before the fall of Muammar Gaddafi in 2011.

The December 17 agreement was signed under intense international pressure from the United Nations, the United States and several major European nations, all of which have been calling persistently for a unity government. The outside interest in Libya is not altruistic: Nations that intervened in 2011 in support of the rebellion against Gaddafi may feel a certain degree of responsibility to help guide the war-torn country towards some kind of workable peace, but their real concern is the threat posed to Europe by the Islamic State of Iraq and the Levant (ISIL) group.

ISIL has taken advantage of the absence of a united government in Libya and of the clashes between opposing militias to carve out a substantial swath of territory along the country's Mediterranean coast. The group has made a base in the oil town of Sirte, Gaddafi's former home, and several other towns along Libya's "oil crescent". In recent weeks, ISIL has carried out a number of successful strikes against the country's oil infrastructure.

The longer Libya is without a united administration, and the longer disparate militias fight each other rather than team up against ISIL, the more successful the group is likely to be. ISIL-controlled territory on Europe's doorstep provides an ideal base from which to launch attacks against European nations, using established people-smuggling routes across the Mediterranean.

To combat this threat, it appears increasingly likely that the US and some European countries will intervene against ISIL in Libya, as they have in Iraq and Syria.

"Some kind of external intervention becomes ever more likely in light of the latest ISIL offensive," said Mattia Toaldo, a policy fellow for the Middle East and North Africa programme at the European Council on Foreign Relations. "Italy, France, the UK and the US have all shown an appetite for intervention."

The European Union "stands ready to support Libya in the fight against violent extremism", according to a statement this month from the European Council. Germany will "not be able to evade responsibility for contributing its share," defence minister Ursula von der Leyen said in an interview last week.

It has been widely reported that French planes have carried out reconnaissance missions over Libya, and according to the state-owned Algerian newspaper El Khabar, the US, France and the UK have informed the Algerian government that they are making preparations to launch air strikes against ISIL in Libya, although Western officials have not committed to this in public statements.

Meanwhile, Robert Ford, the former US ambassador to Syria, said during a hearing of the Armed Services Committee of the House of Representatives that "it will be important ... to help a new Libyan government and to help it control territory, and we will need to be ready to do that".

The more you have attacks like this by ISIL, the less the West will be inclined to wait for an invitation from the government. Mattia Toaldo, analyst

"In an abstract sense, building up a Libyan national army might be desirable in the long run, but it won't get results in the short term, so we may see a shift towards targeted [air] strikes, or enabling strikes by Egypt," Richard Mallinson, a geopolitical analyst at Energy Aspects, told Al Jazeera.

Still, in recent months, outside powers have maintained that they will take action in Libya only at the invitation of a unity government. For this reason, establishing a united administration has become a matter of great urgency.

There are still several procedural steps, however, before such an intervention could happen.

First, the HOR must be convinced to approve the GNA. Next, the GNA needs to establish itself in the country's capital, Tripoli. The final step is an invitation from the GNA requesting foreign intervention.

The problem for the West, however, is that each of these steps is in doubt. The HOR ruled that it will consider an amended proposal in the next 10 days. But it is far from clear that the HOR will reverse its decision. It has yet to express support for the December 17 peace deal or the presidential council.

Meanwhile, there is no sign of the Tobruk government stepping down. Last week, municipal council officials in Bayda, a town near Tobruk where key members of the eastern government are based, ordered the executive to leave the town due to public protests over its failure to provide essential services. The nearby Marj council invited the government to relocate there, according to the Libya Herald.

The GNA, which is currently operating out of a hotel in Tunis, faces an even greater challenge in establishing itself in Tripoli. The General National Congress (GNC) - the parliament affiliated to the Government of National Salvation - is wary of a deal that in effect means it has to give up all legislative authority to the HOR. Some members even suggested scrapping the agreement and starting again.

Still more troubling for the GNA is a statement from the leader of the GNC, Khalifa al-Ghwell, ordering the arrest of members of the 18-strong temporary security team appointed by the presidential council should they stray on to territory controlled by Libya Dawn, a coalition of militias affiliated to the GNC.

"There's an issue of legitimacy for a unity government operating out of Tunis," Mohamed Eljarh, a Libyan national and non-resident fellow at the Rafik Hariri Center for the Middle East, told Al Jazeera. "Many are calling it the government in exile."

READ MORE: Libya's chance to fight off ISIL

Even if the GNA can overcome the odds and somehow secure recognition from the HOR and the compliance of Tripoli to relocate to the capital, it is by no means sure that it will extend the invitation for Western intervention.

"Nobody is thinking about requesting foreign intervention at the moment," Ibrahim Dabbashi, Libya's ambassador to the UN, said last month. "We are willing to fight [ISIL] ourselves."

Ahmed Mateeq, the GNA's deputy prime minister, said in response to UK plans to send 1,000 soldiers to train Libyan troops that "at the moment I don't think we could accept that," and that "Libyans preferred to look after the Libyan soil ourselves".

In some ways, the GNA is in a no-win situation. "I'm not sure the GNA would say 'yes' to an intervention, and even if it did, and it didn't have the support of the Libyan population, it would put it in an uncomfortable position," Toaldo said.

If the GNA does not extend an invitation to the West to intervene, they may consider an intervention without authority from the Libyan government. Last November, following ISIL attacks in Paris, the UN unanimously approved a resolution calling on governments to "take all necessary measures" in the fight against ISIL.

Given that ISIL attacks on Western citizens in Tunis and Sousse last year were carried out by fighters trained at a camp in the Libyan town of Sabratha - and in light of the recent escalation of ISIL attacks in Libya - certain countries may decide that they have sufficient grounds for an intervention without Libyan sponsorship.

"The more you have attacks like this by ISIL, the less the West will be inclined to wait for an invitation from the government," Toaldo said, noting that this would reflect poorly on the legitimacy of the GNA. "If even a limited intervention takes place without the formal assent of the Libyan government, it will show Libyans the irrelevance of the GNA."