Muammar Gaddafi's forces attacked two west Libyan towns, killing dozens, while rebels were pinned down in the east and NATO tried to resolve a dispute over who should lead the Western air campaign.
With anti-Gaddafi rebels struggling to create a command structure that could capitalize on the air strikes against Libyan tanks and air defenses, Western countries had still to decide who would take over command once Washington pulled back in a few days.
In the latest fighting on Tuesday, Gaddafi's tanks shelled the rebel-held western town of Misrata and casualties included four children killed when their car was hit, residents said, adding the death toll for Monday alone had reached 40.
Residents painted a grim picture of the situation in Misrata, under siege by Gaddafi loyalists for weeks, with tanks in the city center and doctors operating on people with bullet and shrapnel wounds in hospital corridors.
"The situation here is very bad. Tanks started shelling the town this morning," a resident called Mohammed told Reuters by telephone from outside the city's hospital, adding: "Snipers are taking part in the operation too. A civilian car was destroyed killing four children on board, the oldest is aged 13 years."
In the first apparent air force casualty of the campaign, a U.S. F-15E crashed in Libya overnight and its two crew members were rescued, the U.S. military said. The crash was likely caused by mechanical failure and not hostile fire, it said.
Explosions and anti-aircraft fire rang out around Tripoli for a third night and state television said several sites in the capital had been attacked by the "crusader enemy."
A Reuters correspondent taken to a naval facility in east Tripoli by Libyan officials saw four Soviet-made missile carrier trucks which were destroyed. They were parked inside a building whose roof had collapsed, leaving piles of smoldering rubble.
"Yesterday six missiles and one bomb from a warplane hit this facility," said Captain Fathi al-Rabti, an officer at the facility. "It was a massive explosion."
REBELS PINNED DOWN IN EAST
Gaddafi forces were trying to seize the western rebel-held town of Zintan near the Tunisian border in an attack using heavy weapons. One resident said 10 people were killed on Tuesday. People fled to seek shelter in mountain caves.
Security analysts say it is unclear what will happen if the Libyan leader digs in, especially since Western powers have made it clear they would be unwilling to see Libya partitioned between a rebel-held east and Gaddafi-controlled west.
Rebels in east Libya were stuck just outside Ajdabiyah on Tuesday, making no advance on the strategic town despite three nights of Western air strikes on the oil-producing state.
At the front line in the desert scrub about 5 km (3 miles) outside the town, gateway to the rebel-held east, fighters said air strikes were helping to cripple Gaddafi's heavy armor.
When asked why rebel units had not advanced toward their objective, which is the eventual taking of Tripoli, Ahmed al-Aroufi, a rebel fighter at the front line, told Reuters: "Gaddafi has tanks and trucks with missiles." Commenting on the air campaign to protect civilians in this uprising against Gaddafi's 41-year rule, Aroufi said:
"We don't depend on anyone but God, not France or America. We started this revolution without them through the sweat of our own brow, and that is how we will finish it."
Washington, wary of being drawn into another war after long campaigns in Iraq and Afghanistan, has ruled out specific action to overthrow Gaddafi, although France said on Monday it hoped the Libyan government would collapse from within.
Facing questions at home about the U.S. military getting bogged down in a third Muslim country and the future of Libya, the U.S. administration has been keen to say the aim of the resolution was to protect civilians.
Commenting on the mission, former U.S. diplomat Nicholas Burns said: "We have to recognize this situation for what it really is -- the first time in American history when we have used our military power to prop up and possibly put in power a group of people we literally do not know."
The United States expects to hand over command of the air campaign in "a matter of days" but has not said which country or organization would take charge.
Britain and France took a lead role in pushing for air strikes which have destroyed much of Libya's air defenses.
President Barack Obama said on Monday the United States would cede operational control within days and NATO would have a coordinating role.
British Prime Minister David Cameron said the intention was to transfer command to NATO but France said Arab countries did not want the U.S.-led alliance in charge of the operation.
NATO ambassadors in Brussels completed plans to help enforce a U.N.-mandated no-fly zone "if needed," but French and Turkish objections again prevented it being put under NATO command.
A NATO role would require political support from all the 28 states. Turkish Prime Minister Tayyip Erdogan, whose country is a NATO member, said on Tuesday that the United Nations should be the umbrella for a solely humanitarian operation in Libya.
Diplomats said France had argued that the coalition led by France, Britain and the United States should retain political control of the mission, with NATO providing operational support, including command-and-control capabilities.
French Foreign Minister Alain Juppe told parliament France and Britain had agreed to put together a "political steering body" of foreign ministers of countries participating in the coalition and the Arab League which would meet in the next few days in Brussels, London or Paris and hold regular meetings.
Two Qatari fighters and two 17 transport aircraft landed in Crete on Tuesday and the U.S. military said the aircraft would be "up and flying" over Libya by the weekend. That will be the first direct outside Arab involvement in the operation.
Four more Qatari aircraft and 24 UAE warplanes were also expected in Crete on their way to a forward base in Sicily.
Rifts were growing internationally over the U.N. resolution, with Russia saying the U.N. Security Council would discuss on Thursday whether Western countries were going beyond the bounds of their authority for intervention. China and Brazil urged a ceasefire amid fears of civilian casualties.
Algeria called on Tuesday for an immediate end to military intervention in Libya, calling the action "disproportionate."
Russian Prime Minister Vladimir Putin said those responsible for civilian deaths in Libya should pray for their souls.
Defense Secretary Robert Gates said on Tuesday during a visit to Moscow some people in Russia seemed to believe what he termed Gaddafi's "lies" about civilian casualties in Libya.
Libyan officials have said air strikes have killed dozens of civilians. They say the rebels are al Qaeda militants assisted by Western powers who are trying to steal Libya's oil.
In Tripoli, Reuters correspondents said some residents, emboldened by a third night of air strikes, dropped their customary praise of Gaddafi and said they wanted him gone.
"My children are afraid but I know it's changing," one man said. "This is the end. The government has no control any more."