The fighting began early Sunday morning as Haftar's forces and troops from the western-backed Government of National Accord (GNA) began fighting in the Wadi Raba farming area.
The UN Mission to Libya today for a truce for two hours in southern Tripoli to evacuate civilians and wounded, it said in a statement without giving details.
Libya has been gripped by unrest since the 2011 uprising that overthrew and killed long-ruling dictator Moammar Gadhafi, and in recent years has been governed by rival authorities in the east and in Tripoli, in the west, each backed by various armed groups.
On Saturday, the head of the GNA accused Haftar of "betraying" him after the latter launched his military offensive on Tripoli.
Pakistan FM claims India planning military aggression
Earlier on Sunday, Pakistan summoned the Indian deputy high commissioner to protest against any "misadventure", Pakistani Foreign Office spokesman Mohammad Faisal said in a tweet.
It's still unclear how much this is a show of force to bolster Gen Haftar's position or a genuine effort to seize Tripoli.
Waldhauser did not discuss where the U.S. forces, who reportedly were taken out of Tripoli on fast amphibious boats, have been relocated to or when they intend to return.
The Indian ambassador in Tunisia has the concurrent charge of Libya as well and the CPRF contingent was deployed as part of a peace-keeping force in Tripoli, the minister added in a subsequent tweet.
"We are agreed that we must use all the possibilities at our disposal to exert pressure on those responsible in Libya especially General Haftar, so that we avoid any further military escalation", German Foreign Minister Heiko Mass told reporters.
In December Haftar met Prime Minister Fayez al-Serraj from the UN-backed government at a conference but refused to attend official talks.
For the first time, forces backing the GNA launched air strikes earlier Saturday on Haftar's self-proclaimed Libyan National Army (LNA) - which vowed to retaliate - around 50 kilometres south of Tripoli.
Sanders to Appear on Fox News for Town Hall on Jobs
It's also about a candidate being able to convince regular people to part with one of their most precious resources: Money. His campaign did not say how much money it had spent and had left in the bank at the end of March.
Fresh fighting has flared near the Libyan capital, Tripoli, between pro-government forces and rebel fighters from the east of the country.
In Libya, the US backs a United Nations-recognized government.
The UN has declared that the gathering will go on as planned.
United Nations envoy Ghassan Salame said on Saturday that the conference planned for 14-16 April would still be held in time, despite the escalation - "unless compelling circumstances force us not to".
The unrest comes ahead of a planned United Nations conference on possible new elections.
The country's oil installations should not be used by any group for political gain, it said.
USA count found no Pakistan F-16 jet missing
The sources said that while one of the ejections was of an IAF MIG 21 Bison , the other was of a PAF aircraft. However, India was unable to present any physical evidence to back up its claim of having downed an F-16.