A major military push south by the Libyan strongman Marshal Khalifa Haftar has left him in the ascendant, and possibly able with international backing to dictate the terms of a future Libyan political settlement, including presidential and parliamentary elections.

Haftar, the head of the Libyan national army, has been strengthened by a successful offensive into the often lawless south-west, and some observers say he is in a better position to dictate terms to his rival Fayez al-Sarraj, the head of the UN-recognised government of national accord in Tripoli.

The push into the Fezzan region has left Haftar in control of two-thirds of the country, most border crossings and many key oil installations, including the large oil fields in the Murzuk basin.

The two rivals met in Abu Dhabi on 27 February and may meet again next week in what looks like a fresh attempt to break the near eight-year on-off civil war that has left the country prey to people-traffickers and militias. The situation in Libya has in turn had huge repercussions for the politics of migration in Europe.

Khalifa Haftar, the military commander who dominates two-thirds of Libya. Photograph: Philippe Wojazer/Reuters

The February meeting, which was attended by the UN special mission, led only to a vague public commitment to hold democratic elections this year, but no date was set. It also led to the lifting of the block on oil production at the al-Sharra oil field, Libya’s largest field.

Sarraj has since said the two men agreed to hold elections this year, and to work toward a civilian settlement. A similar pledge was made last summer to hold elections by December, but the deadline was not met, partly because of disputes about the sequencing of elections, including a referendum on a constitution.

The UN special envoy Ghassan Salamé’s long-nurtured plans to hold a national consultation or conference prior to elections have also been delayed.

The international community has welcomed the dialogue, but some groups in the west fear that under international pressure a weakened Sarraj will be willing to stitch up a deal with Haftar and his backers in the east of the country.

Khalid al-Mishri, the head of the high council of state, and a fierce opponent of Haftar’s, flew to Doha for consultations with the emir of Qatar. Qatar has traditionally backed militia in the west while Egypt, the United Arab Emirates and the French have supported Haftar’s anti-Muslim Brotherhood politics. Mishri claimed Haftar had no interest in democracy and wanted to run the country with the same iron fist deployed by Egypt’s president, Abdel Fatah al-Sisi.

In a sign of his own concern at the turn of events, Sarraj demoted his former chief of staff Abdelrahman al-Taweel and terminated his military service. He was sacked after he appeared to welcome Haftar’s victories in Fezzan.

The former UK ambassador to Libya, Peter Millett, said the Abu Dhabi meeting between Sarraj and Haftar should be seen as part of Salamé’s efforts to revitalise the political process in Libya. Millett said Salamé’s proposed national conference was still the only game in town.

Haftar’s move into the south means that he now controls the majority of Libya’s onshore oil fields, Millett said. “He has to be part of the solution, but he must submit to civilian oversight. If he wants to be president, he would have to run as a civilian, but there is no precedent and no constitutional basis for presidential elections.

“Elections this year must have the necessary security, legislative and constitutional preparations, and they must guarantee the unification of Libya’s political, economic and security institutions. This requires careful and detailed preparations. Salamé is the best person to undertake this task.

“Those who oppose Salamé’s plans are either perusing personal agendas or trying to preserve the status quo for their own selfish ends.” He added that the proposed national conference had to go ahead and “produce a truly national political, economic and security road map that serves the Libyan people as a whole”.

It remains to be seen whether Haftar is truly committed to a democratic process, or whether, as some fear, he will prepare to take further territory in the west before a final push to Tripoli, the headquarters of resistance to him .

The Abu Dhabi meeting appears to have led to an agreement in the short term that Mustafa Sanalla, the chairman of Libya’s National Oil Corp (NOC), could end the self-imposed closure, also known as force majeure, of Libya’s al-Sharra field, capable of producing 300,000 barrel of crude a day. A total of $1.8bn (£1.4bn) in revenue has been lost as a result of its capture by militia protesting against Tripoli’s lack of support for the south.

“This costly episode highlights the importance that the NOC remains independent and free from extortions and armed incursions,” said Sanalla, who also demanded the removal of the “no-fly zone” Haftar has imposed in southern Libya.

French Total is one of the joint owners of the field and there have been reports that French special forces are in the area.