Ahmed al-Mesmari, spokesman for the self-styled Libyan National Army led by Hifter, said 14 troops had been killed since Hifter declared the offensive.
Forces loyal to Libya's UN-backed unity government arrive in Tajura, a coastal suburb of the Libyan capital Tripoli, on April 6, 2019, from their base in Misrata.
Haftar's LNA said its positions were attacked in an air strike south of Tripoli but there were no casualties.
Libyan forces under Khalifa Haftar battled their way to the south of Tripoli on Friday, prompting the UN Security Council and the G7 to demand a halt to the military advance on the capital.More news: United States media report says all of Pakistans F-16s intact; IAF rebuts
Earlier in the day, the LNA claimed on Facebook to have captured three major areas near Libya's capital - Qasr bin Ghashir, Wadi Al Rabi and Suq al Khamis.
The airport, abandoned and largely wrecked when civil war broke out in 2014, is seen as a key strategic target because the modern airport road offers LNA armoured units a wide avenue to reach the city centre.
He met with Gen. Haftar and then told journalists he was leaving Libya "with a deep concern and a heavy heart". "I still hope that it would be possible to avoid bloody confrontation in and around Tripoli and the United Nation will remain available to facilitate any political solution able to unify the Libyan institutions".
Despite the flare-up, United Nations envoy Ghassan Salame insisted Saturday that talks planned to be held next week in Libya would go ahead.
Guterres was deeply concerned after the meeting with Haftar who had ordered his self-proclaimed Libyan National Army (LNA) and allied troops to march on Tripoli.More news: Suspect in Christchurch mosque attack to face 50 murder counts, police say
"With Juan Guaido being stripped of his immunity. we don't want the situation to escalate", German Foreign Minister Heiko Maas said in Dinard on Saturday. "There can be no military solution to the conflict", he said. "They called on LNA forces to halt all military movements, they also called on all forces to de-escalate and halt military activity".
Since Gadhafi's ouster, Libya has been split between rival governments in the east and the west and an array of militias fighting over power and oil fields.
Libya's rival leaders, GNA's Prime Minister Fayez Sarraj and Haftar, agreed in Paris last year to hold elections before the end of the year, but that vote never materialized as the two rival administrations and numerous militias grapple for power.
"We were stabbed in the back", he said Saturday in televised comments, adding that his forces would confront Hifter's troops with "force and determination".
Russian Federation called for "all possible efforts to fully resolve the situation with peaceful political means".More news: Joe Biden jokes about inappropriate touching during a speech
"Capturing Tripoli... remains a possibility" for Haftar, with the support he receives from Saudi Arabia and its allies Egypt and the United Arab Emirates, he said.