VINEYARD HAVEN, Mass. -- President Barack Obama said Moammar Gadhafi and his regime must face the fact that their rule in Libya is over as U.S. leaders monitored the progress of Libyan rebel forces as they moved on Tripoli Sunday.

"The surest way for the bloodshed to end is simple: Moammar Gadhafi and his regime need to recognize that their rule has come to an end. Gadhafi needs to acknowledge the reality that he no longer controls Libya. He needs to relinquish power once and for all," Obama said in a statement.

The White House said Obama was briefed on the latest developments by counterterrorism adviser John Brennan and heard reports from U.S. teams in the rebel stronghold of Benghazi.

Defense Secretary Leon Panetta also received updates on the rapidly unfolding situation.

"Gadhafi's days are numbered," a State Department spokeswoman said Sunday. "If Gadhafi cared about the welfare of the Libyan people, he would step down now."

Associated Press reporters with the Libyan rebels said they moved easily Sunday from the western outskirts of Tripoli into the regime stronghold. A rebel leader said the unit in charge of protecting Gadhafi had surrendered and joined the revolt.

For the past two days, senior U.S. diplomats have had intensive discussions with the Libyan opposition, and with European and NATO allies. The U.S. ambassador to NATO, Ivo Daalder, and the top American diplomat for Europe, Philip Gordon, have been consulting with their counterparts.

Assistant Secretary of State Jeffrey Feltman, the top American diplomat for the Mideast, returned to Cairo Sunday after two days in Benghazi, the de facto capital for the rebels. On Saturday, while in Benghazi, Feltman warned that "the best-case scenario is for Gadhafi to step down now . . . that's the best protection for civilians." Nuland said Feltman's trip underscores continuing U.S. efforts to encourage the rebels "to maintain broad outreach across all segments of Libyan society and to plan for post-Gadhafi Libya." White House spokesman Josh Earnest said the U.S. will remain in close contact with its allies and Libyan rebel leaders. Brennan is with Obama as he vacations on Martha's Vineyard.U.S. officials are poised to assist the opposition as the country moves toward democracy. But it wasn't clear Sunday how close such a transition might be, as Gadhafi and his supporters have vowed to continue the fight.

Looking ahead to a possible rebel victory in the 6-month-old civil war, Sen. John McCain (R-Ariz.), said it will be very difficult to build a united democratic government there, due to the tribal rivalries.

"We've seen the difficulties with other countries who made this transition, but we will be rid of a guy who has the blood of Americans on his hands. We will be rid of a guy who has practiced the worst kind of brutalities. And now it's going to be up to us and the Europeans," said McCain, speaking on CBS' "Face the Nation." McCain said he thinks the opposition forces can ultimately succeed in setting up a new government, aided by revenues from oil. He said he believes it is a "matter of hours, if not days" before Gadhafi falls.

-- Wire services

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