The Libyan government escorted journalists from at least two major news outlets to the scene to view the damaged building, which stands near the iconic Bedouin tent where Gadhafi has been known to entertain foreign guests.
Half of the multistory building was destroyed, and scraps of metal from the missile lay scattered across the area.
Explosions and anti-aircraft gunfire had erupted in the Libyan capital earlier in the night, signaling another round of coalition air assaults.
The military operation began overnight Saturday to enforce a UN Security Council resolution that called for an immediate ceasefire in the fighting between Gadhafi forces and members of the month-old opposition movement.
The resolution authorized a no-fly zone above the North African country and allowed UN members to use "all means necessary" to prevent attacks on civilians.
Despite the international pressure, Gadhafi pledged Sunday to continue fighting. In a phone call to Libyan state television, he said his weapon depots had been opened up to allow civilians to arm themselves against the outsiders.
"We promise you a long war," Gadhafi said.
During a press conference at the Pentagon on Sunday afternoon, U.S. Navy Vice Adm. Bill Gortney said naval ships had launched 124 cruise missiles at military installations along the Libyan coast, followed by air assaults from French, British and American fighter jets and bombers against Gadhafi ground forces and air defences.
Gortney said the initial assault had been "very effective in significantly degrading the (Libyan) regime's air defence capability," including its ability to launch some surface-to-air missiles.
"We now have the capability to patrol the airspace over Libya, and we are doing just that," he told reporters.
Military forces from Spain, Belgium, Denmark and Qatar are joining the military operation under U.S. command, Gortney said, but a coalition of countries would take over command in the coming days.