Heavy anti-aircraft fire is lighting up the skies over Tripoli and the sound of loud explosions is echoing through the Libyan capital after nightfall.

The source of the explosions was not immediately clear, but the gunfire appeared to signal a fourth night of U.S. and European air operations over Libya on Tuesday to enforce a no-fly zone.

In the previous night's operations, the coalition air campaign suffered its first loss with the crash of an American fighter jet in the rebel-held east. Both crew ejected safely as the aircraft spun from the sky.

This latest coalition assault comes after Qaddafi's forces shelled rebels regrouping in the desert dunes outside a strategic eastern city earlier Tuesday, and his snipers and tanks roamed the streets of the last major opposition-held city in the west. 

Disorganization among the rebels could hamper their attempts to exploit the air campaign by U.S. and European militaries, who themselves have struggled to articulate an endgame. Since the uprising began on Feb. 15, the opposition has been made up of disparate groups even as it took control of the entire east of the country.

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Regular citizens — residents of the "liberated" areas — formed an enthusiastic but undisciplined force that in the past weeks has charged ahead to fight Qaddafi forces, only to be beaten back by superior firepower. Regular army units that joined the rebellion have proven stronger and more organized, but only a few units have joined the battles while many have stayed behind as officers struggle to get together often antiquated, limited equipment and form a coordinated force.

The ragtag band of hundreds of fighters who made their way to the outskirts of Ajdabiya on Tuesday milled about, clutching mortars, grenades and assault rifles. Some wore khaki fatigues. One man sported a bright white studded belt.

Some men clambered up power lines in the rolling sand dunes of the desert, squinting and hoping to see Qaddafi's forces inside the besieged city of 140,000 that is the gateway to the east.

"Qaddafi is killing civilians inside Ajdabiya," said Khaled Hamid, a rebel who said he been in Qaddafi's forces but defected to the rebels' side. "Today we will enter Ajdabiya, God willing."

Misrata, the last western city held by rebels, was being bombarded by Qaddafi's forces on Tuesday, his tanks and snipers controlling the streets, according to a doctor there who said civilians were surviving on dwindling supplies of food and water, desperately in search of shelter. Up to 40 people were said to have been killed in the rebel-held city, including four children, according to Sky News.

Adm. Samuel Locklear, who is running Operation Odyssey Dawn, confirms that Qaddafi forces are attacking civilians in Misrata.

Locklear says the U.S. will "pursue all actions necessary" to stop these attacks.

Speaking on condition of anonymity for fear of reprisals if the city falls to Qaddafi's troops, he accused international forces of failing to protect civilians as promised under the United Nations resolution authorizing military action in Libya.

"Snipers are everywhere in Misrata, shooting any one who walks by while the world is still watching," he said. "The situation is going from bad to worse. We can do nothing but wait. Sometimes we depend on one meal per day."

Mokhtar Ali, a Libyan dissident in exile elsewhere in the Mideast, said he was in touch with his father in Misrata and described increasingly dire conditions.

"Residents live on canned food and rainwater tanks," Ali said. He said Qaddafi's brigades storm residential areas knowing that they won't be bombed there. "People live in total darkness in terms of communications and electricity."

The air campaign by U.S. and European militaries that began Saturday has unquestionably rearranged the map in Libya and rescued rebels from what had appeared to be imminent defeat.

A U.S. defense official tells Fox News says the U.S. has fired 161 Tomahawk cruise missiles into Libyan territory since military strikes began, with 24 missiles being fired overnight Monday into Tuesday.

He said the strikes overnight effectively extended the area covered by the no-fly zone, but declined to describe how large the zone had become.

Al Jazeera television reports that one of the heads of Qaddafi's brigade, Hussein El Warfali, has been killed, according to Reuters.

Two tanks belonging to forces loyal to Qaddafi were taken out by NATO jets while retreating from Benghazi, Fox News reports.

U.S. Defense Secretary Robert Gates and others said the U.S. military's role will lessen in coming days as other countries take on more missions and the need declines for large-scale offensive action like the barrage of Tomahawk cruise missiles fired Saturday and Sunday mainly by U.S. ships and submarines off Libya's coast.

France has proposed that a new political steering committee outside NATO be responsible for overseeing military operations over Libya.

French Foreign Minister Alain Juppe says the new body will bring together foreign ministers of participating states -- such as Britain, France and the United States -- as well as the Arab League. It is expected to meet in the coming days, either in Brussels, London or Paris.

Juppe says not all members of the military coalition are members of NATO and "this is therefore not a NATO operation." But he says the coalition would use the NATO's "planning and intervention capabilities."

Not all NATO members are in favor of the no-fly zone and airstrikes against Libya.

The Libyan leader has ruled the North African nation for more than four decades and was a target of American air attacks in 1986.

The Associated Press contributed to this report.