The battle for Tripoli escalated on Sunday as a military assault on the city by the eastern Libyan military commander Khalifa Haftar led to 21 deaths and nearly 90 injuries, and international calls for calm were ignored.

As the fighting neared the capital, the UN issued a plea for a temporary ceasefire to allow the wounded to be evacuated. Hours earlier, the US announced it was withdrawing some of its troops from the country, citing deteriorating “security conditions on the ground”. India also withdrew a group of its peacekeepers, saying the situation in Libya had suddenly worsened.

The international airport 15 miles south of central Tripoli was a scene of fierce battles after Haftar claimed to have seized control of the area from the UN-backed government of national accord.

Haftar’s self-styled Libyan National Army, backed by the United Arab Emirates, is leading a multi-pronged assault on the capital in an attempt to overthrow the Tripoli-based GNA.

The death toll issued by the GNA and confirmed by Tripoli hospitals suggest Haftar’s hopes of an immediate collapse of the GNA’s diverse defences have been dashed. But Haftar appears intent on pressing ahead with a decisive battle that will endanger the chances of a UN-sponsored reconciliation between forces in the east and west of the country.

In a battle already marked by wildly conflicting claims, the LNA said the defences of the Tripoli militia were surrendering, but a spokesman for pro-GNA forces announced a counter-offensive against Haftar’s forces.

The spokesman, Col Mohamed Gnounou, said Operation Volcano of Anger was aimed at “purging all Libyan cities of aggressor and illegitimate forces”, in reference to Haftar’s fighters.

The LNA said it had carried out its first air raid on a Tripoli suburb, defying calls by the international community to halt hostilities. Both sides launched airstrikes over the weekend, with Tripoli residents reporting indiscriminate artillery fire hitting homes across the capital.

In a fast-moving military situation, Haftar’s forces claimed over the weekend to have captured Tripoli’s international airport, in the southern part of the city, but this was denied by the GNA and there was fighting there on Sunday.

Tripoli’s schools were closed for a week and queues formed at petrol stations. The Italian interior minister, Matteo Salvini, said he was concerned for the welfare of Italian employees of oil firms such as ENI.

An air assault was mounted on military vehicles belonging to the GNA presidential council’s Naqlia camp. It is thought Haftar has superior air forces supplied by the UAE.There is also mounting concern in Washington about Russia’s role in Libya, with diplomatic sources recently accusing Moscow of deploying up to 300 mercenaries in eastern Libya to support Haftar.

Speaking before an EU foreign affairs council in Brussels on Monday, the UK foreign secretary, Jeremy Hunt, said he would “work every channel to encourage restraint and avoid bloodshed”, adding there was “no justification for [the] LNA move on Tripoli”.

Calls for sanctions to be taken against Haftar were heard for the first time, including from a former UK ambassador to Libya, Peter Millett. Federica Mogherini, the EU foreign affairs chief, will try to organise a united front at a meeting of the EU foreign affairs council on Monday. Tensions between Rome and Paris over the extent of Emmanuel Macron’s past support for Haftar have been simmering for months.

Q&A What is happening in Libya? Show Hide Libya is on the brink of an all-out civil war that threatens to upend years of diplomatic efforts to reconcile two rival armed political factions. An advance led by Khalifa Haftar, the warlord from the east of the country, has diplomats scrambling and the UN appealing in vain for a truce. The French government, the European power closest to Haftar, insists it had no prior warning of his assault, which is closing in on the capital, Tripoli. The outcome could shape not just the politics of Libya, but also the security of the Mediterranean, and the relevance of democracy across the Middle East and north Africa. For more about the fighting in Libya read our quick guide. Photograph: Hani Amara/X03394

The GNA prime minister, Fayez al-Sarraj, who accused Haftar of treachery, has protested to the French ambassador to Libya, Béatrice du Hellen, about the French support for Haftar. On Saturday Macron spoke to António Guterres, the UN secretary general, and the Élysée insisted he was calling for restraint from all sides.

The US evacuation was the first public acknowledgement that the US had forces in Libya. The US Africa Command said: “The security realities on the ground in Libya are growing increasingly complex and unpredictable.”

The US gave no details of the size of the force, or its mission, but said it might be sent back later. In the last three years US special forces have been deployed, along with British and French elite units, to fight Islamic State in Libya. The US has launched more than a dozen sets of airstrikes against Isis in the southern desert.

Footage on social media showed two fast US navy transport craft manoeuvring off a beach in Janzour, in Tripoli’s western suburbs, sending up plumes of spray as American forces were ferried from the shore.

Air tracking websites show continuing US drone activity over Tripoli, and special forces transport planes regularly shuttle between the western city of Misrata and bases in Italy.

Hopes of a truce rest on decisive western pressure being placed on Haftar’s international backers primarily Egypt, Saudi Arabia and the United Arab Emirates to order Haftar to back down. Haftar has been demanding he is made the nation’s military commander freed from political control. Serraj claimed that in a recent round of talks with Haftar he made major concessions on Libya’s future political structure but that Haftar betrayed those agreements.

Sarraj faces a choice between either seeking to defend the capital and waiting for international diplomatic pressure to force Haftar to retreat, or instead launching offensives of his own, thereby escalating the war and possibly losing international backing. Haftar’s hopes that various groups inside Tripoli would defect to him have so far proved misplaced.

UN mediators continue to urge a ceasefire but some think Haftar is unwilling to compromise. “He has never been interested in the policy process. Even when I used to go and see him, he would say: ‘Security comes first, politics will follow,’” said Millett. “His aim is to take Tripoli. I think they [the UN] should impose sanctions. What other tools do the international community have?”

Jonathan Winer, a former US ambassador to Libya, was also scathing about Haftar’s methods, saying on Twitter: “Haftar has built patronage networks over a five-year period now strengthened by foreign financial support and military support. His goal has long been to take [the] country by mixture of conquest and acclamation and to end ‘politics’ and replace that with military rule.”

On Sunday, US secretary of state Mike Pompeo called for an “immediate halt” to Haftar’s offensive. “We have made clear that we oppose the military offensive by Khalifa Haftar’s forces,” he said in a statement.

Pompeo stressed that there was “no military solution to the Libya conflict,” and urged all parties to “urgently de-escalate the situation.”

Despite the clashes, Ghassan Salamé, the UN special envoy for Libya, claimed that attempts were still being made to hold the national conference on Libya’s future in Ghadames on 14-16 April.