She said: "The attack near Mitiga airport [on Monday] that left many civilians in Tripoli stranded brought into stark focus the imperative for all parties to respect global humanitarian law, and to take all possible measures to protect civilians and civilian infrastructure, including schools, hospitals and prisons".
The LNA has conducted air strikes on the south of the city as it seeks to advance along a road from a disused former worldwide airport.
The Libyan National Army, led by the former officer in Kaddafi's army, said that 19 of its soldiers had been killed in the past few days, with its tightened control over the internationally recognised government in Tripoli.
While fighting near the capital continues, a United Nations envoy said he does not see a peace conference taking place as scheduled next week.
On Sunday, Marine Corps Gen. Thomas Waldhauser, the head of U.S. Africa Command said the United States has temporarily withdrawn some of its forces from Libya due to "security conditions on the ground".
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The Israeli prime minister was asked if he was familiar with the details of the US plan, replying he knew "what should be in it". The West Bank remains under Israeli military occupation with limited Palestinian self-rule.
Tensions in the country have risen after General Khalifa Haftar, whose Libyan National Army (LNA) controls most of eastern Libya, launched a campaign to take over Tripoli where the UN-backed government is based.
"We assure you that the LNA will be embraced by the residents of Tripoli".
A Reuters correspondent in the city centre could hear gunfire in the distance southwards.
The United Nations said 2,800 people were displaced by clashes and many more could flee, though some were trapped.
Al-Serraj, 59, who comes from a wealthy business family, has run the Tripoli government since 2016 as part of UN-brokered deal boycotted by Haftar.
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Also Monday, U.N. envoy Ghassan Salame said he met with Fayez Sarraj, head of the government in Tripoli, to discuss how the U.N. mission "can assist at this critical and hard juncture".
The UN, US and European Union and the Group of Seven economic bloc have all called for a ceasefire.
Mr Haftar casts himself as a foe of extremism but is viewed by opponents as a new dictator in the mould of Gaddafi, whose four-decade rule was marked by torture, disappearances and assassinations. Its elite Saiqa (Lightning) force, numbers some 3,500, while Haftar's sons also have well-equipped troops, LNA sources say.
Libya has become the main conduit for African migrants and refugees trying to reach Europe, with many detained if their journey fails and they are sent back.
Islamic State staged some high profile attacks in Tripoli previous year, but the militant group has largely retreated to the desert of southern Libya since the loss of its former stronghold in Sirte in late 2016.
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Forces allied to the Tripoli government meanwhile announced their own operation called "Volcano of Anger" to defend the capital, a spokesman said, without giving details.