Officials in the capital say they are open to international efforts that would bring an end to four months of fighting between forces loyal to the longtime leader and rebels who control the eastern third of the country along with pockets in the west.
But they insist that Qaddafi will not bow to international pressure to push him aside.
"We don't accept anything that may be done against him. He is a red line in our discussions," Prime Minister al-Baghdadi al-Mahmoudi said Thursday. Any deal that would partition the country is unacceptable, he added.
Al-Mahmoudi told reporters that the Libyan government has held a number of "preliminary meetings" with officials based in the eastern rebel-held city of Benghazi. He said the talks took place abroad, including in Egypt, Tunisia and Norway, but he did not provide specifics.
One of Qaddafi's sons told an Italian newspaper that while his father would not seek exile, elections under international supervision could offer a way out. A vote could be organized within three months, he said.
The son, Seif al-Islam, told Corriere della Sera that Qaddafi would step aside if he lost, which the son said was unlikely. He acknowledged, however, that "my father's regime as it developed since 1969 is dead."
"It's a little late for any proposals by Qaddafi and his circles for democratic change," she said Thursday. "It's time for him to go."
Qaddafi's son, once groomed to succeed the elder Qaddafi, has served as one of his main spokesmen during the conflict. Like Qaddafi himself, he has been heard from rarely in recent weeks.
Russia's envoy to Libya met with senior government leaders in Tripoli -- but apparently not Qaddafi himself -- hours after NATO warplanes pounded the area near the leader's Bab al-Aziziya compound.
Russian envoy Mikhail Margelov met in Tripoli with al-Mahmoudi and Foreign Minister Abdul-Ati al-Obeidi.
Last week, Margelov visited the Libyan rebel stronghold of Benghazi and said that Qaddafi has lost his legitimacy. However, the envoy also said NATO airstrikes are not a solution to Libya's violent stalemate.
Reporters taken to a bombing site around midday saw Margelov there in the company of government officials.
The Interfax agency quoted Margelov as saying, after meeting the foreign minister, that he was told "Qaddafi is not prepared to leave, and the Libyan leadership will talk about the country's future only after a cease-fire." The foreign minister also said, according to Margelov, that the African Union should be "the main force" in reaching a resolution.
Spain ordered the expulsion of the Libyan ambassador in Madrid, saying Qaddafi's regime no longer has legitimacy. A Foreign Ministry statement Thursday said the government gave Ajeli Abdussalam Ali Breni 10 days to leave the country. Three other diplomatic staffers were also ordered out.
At least three NATO bombing runs shook the Libyan capital late Thursday. The targets were not immediately known and there was no report of casualties.
NATO launched its air campaign nearly three months ago under a United Nations resolution to protect civilians. What started as a peaceful uprising inside the country against Qaddafi and his more than four-decade rule has become a civil war.
Fighting between government forces and the rebels had reached a stalemate until last week when NATO launched the heaviest bombardment of Qaddafi forces since the alliance took control of the skies over Libya.
Tunisian army official Mokhtar Ben Nasr said the number of Libyans fleeing has mounted in recent days, with 6,330 Libyan refugees crossing into Tunisia earlier this week. Dozens of Libyan soldiers also have defected to Tunisia by boat, the state news agency there reported Wednesday.
A Tunisian official said a lieutenant colonel was the latest Libyan officer to desert Qaddafi's army and flee across the border.
The official told The Associated Press Thursday that the officer took a desert road through the Sahara to cross the border near the town of Ben Guerdane, where he was stopped by a Tunisian national guard unit.
The officer told authorities that he wanted to join his family. They had earlier fled Libya for the Tunisian island of Djerba, the official said, speaking on condition of anonymity because he was not authorized to talk to the press.
Its 32-page report to Congress argues that because the U.S. has a limited, supporting role in the NATO-led bombing campaign in Libya and American forces are not engaged in sustained fighting, the president is within his constitutional rights to direct the mission on his own.
The report appeared to do little to quell congressional criticism. A spokesman for House Speaker John Boehner, R-Ohio, said the White House was using "creative arguments" that raised additional questions.