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The Obama administration reached out Tuesday to the Libyan rebels and said Moammar Gadhafi would "inevitably" be forced from power as the U.S.-backed NATO coalition launched a withering bombardment on the Libyan leader's stronghold of Tripoli.

The NATO airstrikes struck in rapid succession shortly after midnight, setting off more than 20 explosions in the most intensive bombardment yet of the Libyan capital. Plumes of acrid-smelling smoke rose from an area around Gadhafi's sprawling Bab al-Aziziya compound in central Tripoli.

The punishing attack came after U.S. Secretary of State Hillary Rodham Clinton declared the Libyan leader's ouster was inevitable. Speaking late Monday in London, she said: "We do believe that time is working against Gadhafi, that he cannot re-establish control over the country."

"The opposition has organized a legitimate and credible interim council that is committed to democratic principles, their military forces are improving and when Gadhafi inevitably leaves, a new Libya stands ready to move forward," she said.

The U.S. administration bolstered the standing of the rebel National Transnational Council, calling it a "legitimate and representative and credible" body and extending an invitation Tuesday for it to set up a representative office in Washington — though the overture stopped short of formal U.S. recognition.

The international community has stepped up both the air campaign and diplomatic efforts against the regime in a bid to break a virtual stalemate between the rebels in the east and Gadhafi, who maintains a stranglehold on most of the west.

NATO Secretary General Anders Fogh Rasmussen told journalists traveling with him Tuesday in Herat, Afghanistan, that he hopes a "solution" will soon come to end the fighting in Libya.

"We are trying to protect the citizens and the population against attacks, and to that end, we have taken out a significant amount of Gadhafi's military capacity," Fogh Rasmussen said. "I feel confident that this combination ... of high military pressure and real political pressure will eventually lead to the collapse of the regime."

Government spokesman Moussa Ibrahim said at least three people were killed and dozens wounded in the NATO strikes that targeted what he said were buildings used by volunteer units of the Libyan army.

NATO said in a statement the precision-guided strikes hit a vehicle storage facility that had been used in "attacks on civilians." It was not immediately clear if the facility was the only target hit in the barrage. Gadhafi's Bab al-Aziziya compound, which includes a number of military facilities, has been pounded repeatedly by NATO strikes.

"We thought it was the day of judgment," said 45-year-old Fathallah Salem, who had rushed his 75-year-old mother to the hospital after she suffered shock. He said his home trembled and the youngest of his seven children screamed in terror at the sound of the rolling blasts.

The U.S. launched the international air campaign on March 19 after the United Nations authorized "all necessary measures" to protect civilians following Gadhafi's brutal suppression of the popular uprising against his rule. NATO, which has taken over the airstrikes, says it has been doing its best to minimize the risk of collateral damage.

Critics argue that NATO has overstepped its mandate and is trying to bring about Gadhafi's ouster.

As the alliance has escalated and widened the scope of its strikes over the past weeks, many countries have moved to build closer ties with the rebel movement.

Jordan's Foreign Minister Nasser Judeh announced Tuesday that his country had recognized the rebels' National Transitional Council as the legitimate representative of the Libyan people and would soon name a permanent envoy in Benghazi.

Several other countries, including France and Italy, have recognized the rebel administration, while the United States, European Union and others have established a diplomatic presence in Benghazi.

Jeffrey Feltman, the assistant secretary of state for Near Eastern Affairs, said he had extended an invitation on Obama's behalf to the rebels to establish a representative office in Washington — a move he called "an important milestone in our relationship with the National Transitional Council."

But he stopped short of formal recognition because of what he called the council's temporary nature, saying its "job is to go out of business as soon as possible." Council members stress they will represent Libyans only until Gadhafi can be defeated and democratic elections held.

"We are not talking to Gadhafi and his people. They are not talking to us. They have lost legitimacy," Feltman told reporters during a visit to the de-facto rebel capital of Benghazi.

Feltman also said he expects Congress to vote soon to allow frozen regime assets in the U.S. to be used for humanitarian aid in Libya.

Rebel leaders welcomed the diplomatic contact, but said only better weapons will help them defeat Gadhafi.

"It is just not enough to recognize (us) and visit the liberated areas," spokesman Abdel-Hafidh Ghoga told The Associated Press. "We have tried very hard to explain to them that we need the arms, we need funding, to be able to bring this to a successful conclusion at the earliest possible time and with the fewest humanitarian costs possible."

Rebels now control the populated coastal strip in the country's east and the western port city of Misrata, which Gadhafi's forces have besieged for months. They also control pockets in Libya's western Nafusa mountain range.

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Faul reported from Benghazi. Associated Press writers Jamal Halaby in Amman, Jordan, and Patrick Quinn in Herat, Afghanistan, contributed to this report.