(CNN) -- Forces loyal to embattled Libyan strongman Moammar Gadhafi launched a new attack on the rebel-held city of Misrata on Wednesday, with anti-government forces reporting intense shelling from three sides of the city.
Thousands of government troops attacked around 6 a.m. (11 p.m. Tuesday ET), with 13 rebels reported dead by evening. Mohamed Mokhtar, a rebel fighter wounded in Wednesday's fighting, accused government troops of infiltrating rebel lines in cars bearing rebel flags.
Dr. Khaled Abu Falgha, a spokesman for Misrata's Hekma hospital, said it was the bloodiest day in a week in the besieged city. More than 1,000 people are believed to have been killed since the fighting began there in February, including 686 registered residents of the city, he said.
Rebel fighters returning from the front lines reported that their defenses were holding up under the onslaught, however.
The assault followed a day of intense bombardment of Libya's capital by the NATO alliance, which intervened in the conflict in March under a U.N. mandate to protect civilians as Gadhafi tried to crush the revolt against him. Libya's government said 60 missiles struck the capital city, killing at least 31 people, including a number of civilians, and wounding dozens more.
NATO Secretary General Anders Fogh Rasmussen reiterated Wednesday that the alliance is doing all it can to avoid civilian casualties. But he told reporters from allied headquarters in Brussels, Belgium, that NATO could continue the airstrikes "for as long as it takes to bring this crisis to an early conclusion."
Rasmussen said NATO bombing has saved lives in Libya, and that the alliance has the resources to extend its military mission for another 90 days past the end of June.
It is time to start planning for what to do after Gadhafi's departure "because Gadhafi's reign of terror is coming to an end," he said.
Pressed by reporters on why airstrikes would be able to dislodge Gadhafi when "the history of the last 30 years" shows that air attacks alone do not win wars, Rasmussen offered no clear answer, saying only, "We have no intentions to put troops on the ground."
For his part, even as NATO airstrikes bombarded his Tripoli compound, Gadhafi vowed Tuesday that "we will not surrender."
"I am now speaking as planes and bombs fall around me," Gadhafi said in a live audio broadcast on state television. "But my soul is in God's hand. We will not think about death or life. We will think about the call of duty."
The Gadhafi compound was under "intensive continuous bombardment," according to state TV, which reported buildings and infrastructure were destroyed. But government spokesman Musa Ibrahim said the allied campaign "is failing miserably."
"No one has the right to shape Libya's future except for Libyans," he said.
Ibrahim said Tuesday's morning blasts hit the popular guard compound and the revolution compound, which are military barracks near Gadhafi's Bab al-Aziziya compound. The spokesman said attacks Tuesday and Wednesday hit state television buildings, killing two people and wounding 16.
NATO disputed the account.
"We did not target or hit the Libyan broadcast facilities. What we did target was the military intelligence headquarters in downtown Tripoli," the alliance said. "The story coming from Libyan officials that we targeted and hit the state broadcaster's building is bogus."
CNN's Amir Ahmed, Richard Allen Greene, Raja Razek, Dan Rivers and Jonathan Wald contributed to this report.