There was no immediate word on the targets in the new round of strikes. The heavy chatter of anti-aircraft defenses began soon after nightfall.
U.S. Defense Secretary Robert Gates said the U.S. expects to turn control of the Libya military mission over to a coalition - probably headed either by the French and British or by NATO - "in a matter of days."
The U.S. military says the first air assault by the U.S. and its allies the night before - including airstrikes by long-range bombers and a shower of Tomahawk cruise missiles - was successful, though it did not fully eliminate the threat from Libyan air defenses.
Following Saturday's attack, Libyan leader Moammar Gadhafi is vowing to stay in the fight for the long haul.
An administration building a few yards from Gadhafi's tent in his huge personal compound was hit and badly damaged late Sunday.
U.S. officials said that Gadhafi was not being targeted.
While the U.S. was leading the initial onslaught, officials made it clear that America would quickly step back into a supporting role and shift command to its European and Arab partners.
Gadhafi said /*Libya*/ will fight back against what he believes is unwarranted retaliation from international forces.
"This is an aggression that has no justification. We promise you a long war. We are not worried. We are not afraid," the leader said in a statement following Saturday's attacks.
The attack to enforce a U.N.-mandated no-fly zone was triggered by rebel forces being overwhelmed by Gadhafi's superior military force.
The strikes began with 112 Tomahawk cruise missiles launched mostly from U.S. ships and submarines onto more than 20 radar systems, communications centers and surface-to-air missile sites in Libya. The first missiles struck at 3 p.m. ET.
The U.S. has at least 11 naval vessels in the Mediterranean, including three submarines, two destroyers, two amphibious warfare ships and the USS Mount Whitney, a command-and-control vessel that is the flagship of the Navy's 6th Fleet. Also in the area are Navy P-3 and EP-3 surveillance aircraft, officials said.
Authorities said the cruise missile assault was the leading edge of a coalition campaign, named Operation Odyssey Dawn.
There are reports that the U.S. took out a major Libyan airfield in the first wave of assaults.
Early Sunday, the U.S. military announced that Navy electronic warfare aircraft and Marine Corps attack jets joined the international assault. Navy EA-18G Growlers launched from unspecified land bases to provide electronic warfare support over Libya. Marine AV-8B Harriers from the USS Kearsarge sailing in the Mediterranean conducted strikes against Gadhafi's ground forces and air defenses.
/*President Barack Obama*/ specifically outlined America's involvement in Libya.
"So we must be clear, actions have consequences. And the writ of the international community must be enforced. That is the cause of this coalition. As a part of this effort, the United States will contribute our unique capabilities at the front end of the mission to protect Libyan civilians and enable the enforcement of a no-fly zone that will be led by our international partners," the president said.
The next phase in the military action will be enforcing the no-fly zone over rebel-held Benghazi.
Once that second phase begins, the U.S. will hand off command of the operation to a coalition partner.
Sunday, top U.S. military officials said the international coalition can achieve its goals in Libya, but the chance that Gadhafi clings to power is certainly a potential outcome.
Adm. Mike Mullen, chairman of the Joint Chiefs of Staffs, said on NBC's "Meet the Press" that the no-fly zone was now in place, with Gadhafi having put no aircraft in the sky.
Mullen also said he hasn't seen any reports of civilian casualties as a result of the coalition's military operation and that Gadhafi has resorted to using human shields in an attempt to prevent further attacks.
Meanwhile, Pope Benedict XVI issued an urgent appeal Sunday to military and political leaders to consider the safety of Libyan civilians and ensure they have access to emergency aid.
As the world watches Operation Odyssey Dawn unfold in Libya, many are wondering what's next for the besieged country.
In Los Angeles, more than two dozen opponents of the Libyan dictator converged Saturday, waving American and Libyan flags and voicing their support for the missile strikes.
"I'm so happy," said demonstrator Fatima Shalluf of Torrance. "I hope it helps and I hope Gadhafi will finally leave so we can have a free and democratic Libya."
In Hollywood, hundreds rallied and marched through the streets Saturday, marking the eighth anniversary of the Iraq war. Protesters also denounced the U.S. military action in Libya and called for troops to be pulled out of Iraq and Afghanistan.
Experts say that the one thing that is certain is that Libya's political future must be determined by the Libyan people.
"Whether they're going to take the nationalist route, whether they're going to take a regionalist route, whether they split into even further fragments, we just can't force it," said Dr. James Gelvin, a professor of Middle Eastern history at the University of California, Los Angeles.
The Associated Press contributed to this report.
