Battles Tuesday night and Wednesday morning left rebels in control of the northern, eastern and western perimeters of the airport compound, leaving only the south where Gaddafi's troops would face fierce resistance if they wanted to fight their way out.
Insurgent forces captured 40 Grad rockets from the regime troops, whose mortar fire injured 13 rebels, the AFP correspondent said.
It was unclear if any regime fighters were killed or wounded, but rebels said they had captured one Mauritanian mercenary in Gaddafi's employ, although AFP could not confirm this.
Libyan rebels said they had taken the town of Zareek, about 25 km (15 miles) west of Misrata, but were still trying to extinguish fires at fuel storage tanks caused by a government attack last week.
Misrata, besieged by Gaddafi's forces for eight weeks, is strategically important to rebel hopes of overthrowing the Libyan leader because it is the only city they hold in the west of the North African country.
NATO launched missile strikes on Tuesday in the Tripoli area on targets that appeared to include Gaddafi's compound, witnesses said. NATO said later it carried out a strike against a government command and control post in the capital.
After two months of revolt linked to this year's uprisings in other Arab countries, the war has reached a stalemate. Rebels hold Benghazi and other towns in the oil-producing east while the government controls the capital and almost all of the west.
Thousands have been killed in the fighting.
The government says the rebels are armed criminals and al Qaeda militants and that the majority of Libyans support Gaddafi, who has been in power since 1969.
He has not appeared in public since April 30, when a NATO air strike on a house in the capital killed his youngest son and three of his grandchildren.
The rebels, battling against Gaddafi's superior firepower, said government forces bombarded a residential area outside the Misrata on Tuesday and that 100 rebel fighters were wounded in a separate shelling attack.
Rebels had surrounded Gaddafi's forces at the airport and an air force academy near the southern neighbourhood of al Ghiran where the two sides fought fierce battles on Monday, a witness and a rebel spokesman said.
"The plan is to drive out Gaddafi's forces from the airport and the air force academy where they are now trapped," rebel spokesman Abdelsalam said by phone from Misrata.
It is difficult to independently verify accounts of events in Misrata.
The proximity of Gaddafi's forces to civilian areas made it hard for NATO to carry out its mandate of protecting civilians, Brigadier-General Claudio Gabellini, chief operations officer of NATO's Libya mission, told reporters in Brussels.
He said NATO had still managed to destroy more than 30 military targets in Misrata since April 29.
"Pro-Gaddafi forces have continued to shell the citizens of Misrata with long-range artillery, mortars and rockets, indiscriminately firing high explosive rounds into the city," said Gabellini.
The Libyan government says NATO's intervention is an act of colonial aggression by Western powers bent on stealing the country's oil. The war has caused misery for tens of thousands forced to flee overland or by boat.
Aid agencies say witnesses reported a vessel carrying between 500 and 600 people foundered late last week near Tripoli and that many bodies were seen in the water.
Before that, about 800 people had gone missing since March 25 after trying to escape from Libya, according to the U.N. High Commissioner for Refugees. Most were from sub-Saharan Africa.
Libyan officials said on Tuesday four children had been wounded, two of them seriously, by flying glass caused by blasts from NATO strikes overnight.
Officials showed foreign journalists a hospital in the capital where some windows were shattered, apparently by blast waves from a NATO strike that toppled a nearby telecommunications tower.
The journalists were also taken to a government building housing the high commission for children, which had been completely destroyed. The old colonial building had been damaged before, in what officials said was a NATO bombing on April 30.
"The direction of at least one blast suggests Gaddafi's compound has been targeted," said one witness.
Libyan officials said the government released 120 rebel prisoners on Tuesday. A Reuters reporter in Tripoli saw the men rejoining their families at a government-organised event.