NATO rained scores of bombs on the Libyan capital Tuesday in by far its heaviest attack on Tripoli since its campaign began, but Moammar Gaddafi responded swiftly with a vow that his people would never surrender.

Huge explosions rattled windows and nerves across Tripoli during a rare daytime bombardment that lasted from late morning into the night. Jets buzzed overhead, and plumes of dark gray smoke billowed into the sky. The Libyan government said 60 bombs fell on the city, killing 31 “soldiers, guards and civilians.” Reporters in Tripoli counted more than 40 explosions.

President Obama said that NATO had made significant progress in its campaign and that it was “just a matter of time” before Gaddafi was forced from power.

But Gaddafi phoned Libyan state television late in the afternoon to call his supporters onto the streets “in their millions” to show their defiance. “We will not kneel, we will not surrender,” he said. “We have only one choice, until the end: Victory or death, it doesn’t matter.”

After Gaddafi’s 10-minute address, cars sped past the Rixos Hotel — where foreign journalists are staying — honking their horns and waving the green flags of the Libyan government. A few hundred people gathered outside Gaddafi’s sprawling Bab al-Aziziyah headquarters complex, and a smaller crowd also assembled outside the Rixos, shouting slogans and firing Kalashnikov rifles into the air.

“We are stronger than your missiles, stronger than your planes, and the voice of the Libyan people is louder than explosions,” Gaddafi said, adding that he was ready to send 250,000 to 500,000 armed Libyans to cleanse the country of the rebels, whom he called “armed gangs” and “bastards.”

Tuesday has been reported to be Gaddafi’s 69th birthday, but neither government nor NATO officials seemed aware of the significance of the date.

NATO said it was hitting the center of Gaddafi’s military command-and-control facilities and warned that the bombing campaign would intensify.

The Libyan government said NATO had struck “military and semi-military” sites, including centers for the Popular Guard and the Revolutionary Guard, two militias responsible for internal security. Officials also showed journalists one building inside Bab al-Aziziyah that had been leveled; reporters spotted a body in the rubble.

Government spokesman Moussa Ibrahim said NATO leaders were “losing their heads” and complained that not a single representative from Britain, France or the United States has asked to visit Libya and talk to the government since the crisis began, despite the government’s repeated assertion that it was ready for dialogue, peace and elections.

“No one has ever talked to us from the countries that are bombing us,” he said. “Isn’t that weird?”

Analysts said that NATO appeared to be targeting the country’s internal security apparatus in an effort to encourage Gaddafi’s opponents to rise up in Tripoli. Although open dissent has been growing and some demonstrations have taken place in the capital in the past two weeks, a widespread uprising there still seems unlikely anytime soon.

“As the people of Tripoli break the fear factor, it is possible what NATO is doing is degrading the regime’s ability to crack down on dissent,” said Shashank Joshi of the Royal United Services Institute in London.

Despite growing congressional reticence about U.S. military action in Libya, most Americans continue to support U.S. participation in enforcing the Libya no-fly zone, according to a new Washington Post-ABC News poll. But only a small minority support expanding that mission to seek Gaddafi’s removal from power, as NATO has done.

Fully 58 percent of respondents approve of the participation of U.S. military aircraft in support of the no-fly zone and to attack Libyan forces threatening civilians, a level that has changed little over almost three months of bombing. Support also remains consistent across party lines, with about six in 10 Democrats, Republicans and independents alike in favor of that mission.

But only half of that number support an expansion of the mission to include attempting to remove Gaddafi from power.

Last week, NATO extended its military mission in Libya for three months. But as the two sides dug themselves in deeper for an escalation of the military confrontation, efforts also continued to find a diplomatic solution to the crisis.

Libya’s foreign minister, Abdul Ati al-Obeidi, flew to Beijing for talks, a few days after the Chinese government met with representatives of the rebellion.

U.N. special envoy Abdul-Illah Khatib met with Libyan officials in Tripoli, while Russia’s Africa envoy, Mikhail Margelov, met with the head of the rebel Transitional National Council, Mustafa Abdel Jalil, in Benghazi.

“We are ready, if it’s possible, to act as middlemen in establishing an internal Libyan political dialogue,” Margelov told a news conference. “We . . . believe that Gaddafi has lost his legitimacy after the first bullet shot against the Libyan people.”

Meanwhile in Geneva, a Libyan rebel diplomat said that Labor Minister Al-Amin Manfour, who had been representing Libya at the International Labor Organization’s annual meeting, had defected and joined the rebels, the Associated Press reported.

Staff writer Jon Cohen in Washington contributed to this report.