Celebrations broke out in Tripoli last night after the presidents of Libya's rival parliaments met in Malta and declared they would not sign a UN-brokered agreement, but they would work afresh on the setting up of a new unity government.

“We came here to announce to the world that we are able to solve our problems ourselves, with the help of the international community, but we will not accept foreign intervention against the will of the Libyan people,” said Aguila Saleh Issa, president of the House of Representatives in Tobruk after the meeting at the Auberge de Castille.

Nouri Abusahmain, president of the Tripoli-based General National Council, appealed for the international community to take into consideration the progress made yesterday and allow the country more time to form an effective unity government.

“Acting hastily on this matter will only lead to more problems in future,” he said.

Aguila Saleh Issa, left, and Nouri Abusahmain with Joseph Muscat last night. Photo: Steve Zammit Lupi

Despite rejecting the UN deal, the two presidents announced they had reached agreement on a broad range of issues during their hour-long meeting.

The two sides agreed to form unity committees to work from today towards a new agreement under the umbrella of the UN mission in Libya, although the leaders did not discuss the specifics of how a new government would be formed.

They also agreed on the need to fight terrorism in all its forms and also to strengthen the fight against human trafficking and irregular migration.

The country is effectively split between the internationally recognised government, which is exiled in Tobruk, and the self-declared administration in the capital, Tripoli.

The UN accord proposes a unity government based in Tripoli that will enjoy international support. The two sides had set today as a deadline to reach an agreement following a year of talks.

The political and security vacuum has also allowed Islamic State to gain a foothold in Libya, where the group now controls the coastal city of Sirte.

Sources said that yesterday’s talks took place in Malta on the request of the Libyan authorities. The talks were planned to take place last Saturday but were called off when the Tobruk representative failed to turn up.

Malta did not participate in discussions but provided the location and logistics.

Both sides yesterday thanked Malta for its support, although Mr Abusahmain expressed disappointment that the meeting had not taken place in a Libyan city.