The explosions, just before midnight on Tuesday, hit the southern residential district of Abu Salim near a disused airport, killing at least four people and adding to a death toll the United Nations puts at more than 800.
"Horrible night of random shelling of residential areas. For the sake of 3 million civilians living in Greater Tripoli, these attacks should stop. NOW!" tweeted U.N. envoy Ghassan Salame, who lives in Tripoli and has been pushing a peace plan in vain.
Both sides blamed each other for the attack.
Haftar and his eastern Libyan forces have cast their advance as part of a campaign to restore order and defeat jihadists in nation gripped by anarchy since the 2011 overthrow of Muammar Gaddafi.
But the internationally-recognized Tripoli government of Prime Minister Fayez al-Serraj - which has kept him at bay in the southern suburbs - views the 75-year-old general as a dangerous would-be dictator in the Gaffafi mould.
The United Nations' humanitarian agency the OCHA said thousands of civilians were trapped in southern districts of Tripoli due to the fighting.
Rescuers and aid workers were having difficulty reaching them and electricity, water supplies and telecommunications have been badly disrupted, it said in a statement.
Nearly 20,000 people have now fled their homes, some seeking shelter elsewhere in the capital but most heading out of the city. At least 14 civilians had been killed and about 36 wounded during the offensive, the OCHA said.
Prime Minister Serraj toured the damaged area on Wednesday morning, his office said. Abu Salim lies about 8 km (5 miles) from the city center, behind the front line of pro-Serraj forces blocking LNA troops to their south.
"This is a senseless war against civilians," one man, Mohamed, told Reuters among angry people in the area, where houses and cars were damaged.
"I saw the rockets fall. This is a crime by Khalifa Haftar," said another man who gave his name as Abdelrazaq.
International powers are aghast at the flare-up in Libya, which has scuppered a United Nations' peace plan, threatens to disrupt oil supplies from the OPEC nation, and may unleash a new wave of illegal migration across the Mediterranean to Europe.
But no common position has emerged given different sympathies towards the factions round the Gulf and Europe.
Italy's Interior Minister Matteo Salvini said Haftar's offensive had heightened the risk of militants joining migrant boats in the Mediterranean heading for his country.
"Islamist terrorist infiltration is no longer a risk, it has become a certainty: it is therefore my duty to reiterate that no docking will be allowed on Italian shores," Salvini, leader of the anti-immigrant League party, said in an interview with Radio Rai 1.
Rome has blocked charity boats that rescue migrants in the Mediterranean from docking at Italian ports, saying the ships are aiding people smugglers and encouraging mass, unregulated immigration. The charities have denied breaking any laws.
The government has also accused the European Union of leaving Italy isolated in dealing with the migration crisis of recent years. Since Salvini took office last June, the number of new migrant arrivals has fallen more than 90 percent.
"Italy is working day and night for peace, dialog and a ceasefire, so common sense might prevail," added Salvini of the Libya conflict. Rome is pushing for Haftar to halt his advance.Italy, with considerable oil interests in Libya, supports Serraj, bringing tensions with France which has backed Haftar in the past.