OAK BLUFFS - US President Barack Obama said on Sunday that Muammar Gadhafi's rule was showing signs of collapse and called on the Libyan leader to relinquish power to avoid further casualties.

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

The United States has played a supporting role in the NATO campaign that started in March to protect protesters and other civilians from attacks by Gadhafi's forces, providing technical support and intelligence information to help air strikes.

Obama said the United States got involved to shield the Libyan people from humanitarian crisis.

In his Sunday evening statement, Obama called for the Transitional National Council rebels in Libya to take control and do all possible to avoid further casualties and help smooth genuine democracy.

"At this pivotal and historic time, the TNC should continue to demonstrate the leadership that is necessary to steer the country through a transition by respecting the rights of the people of Libya," he said.

Obama, who is on vacation with his family on the island of Martha's Vineyard off the Massachusetts coast, also pledged further involvement in the North African country.

"We will continue to work with our allies and partners in the international community to protect the people of Libya and to support a peaceful transition to democracy," Obama said.

Obama's statement came shortly after rebel forces streamed through the Libyan capital of Tripoli, waving flags and firing into the air. The rebels said the city was under their control except Gadhafi's Bab Al-Aziziyah stronghold, according to al-Jazeera Television.

Two of Gadhafi's sons were captured by the rebels.

The US State Department repeated a call for Gadhafi to step aside.

"We continue efforts to encourage the TNC to maintain broad outreach across all segments of Libyan society and to plan for post-Gadhafi Libya," State Department spokeswoman Victoria Nuland said.

"Gadhafi's days are numbered. If Gadhafi cared about the welfare of the Libyan people, he would step down now."