U.S. President Barack Obama said on Sunday that Libyan leader Muammar Gaddafi's rule in the country has come to an end, urging him to relinquish "power once and for all."

"Tonight, the momentum against the Gaddafi regime has reached a tipping point," Obama said in a statement issued by the White House. "The Gaddafi regime is showing signs of collapsing."

"Muammar Gaddafi and his regime need to recognize that their rule has come to an end," he said, adding that "Gaddafi needs to acknowledge the reality that he no longer controls Libya."

Obama also called on the main opposition group, the National Transitional Council (NTC), to "steer the country through a transition by respecting the rights of the people of Libya, avoiding civilian casualties, protecting the institutions of the Libyan state, and pursuing a transition to democracy that is just and inclusive for all of the people of Libya."

He said the people of Libya are showing that the pursuit of dignity and freedom is far stronger than the "iron fist of a dictator."

Obama vowed that the U.S. will continue to "insist that the basic rights of the Libyan people are respected" and "support the peaceful transition of democracy."

Obama, who is on vacation on the island of Martha's Vineyard off the Massachusetts coast, has been closely monitoring the developments in Libya on Sunday.

His statement came after Libyan rebel forces have seized control of much of Tripoli and taken two of Colonel Muammar Gaddafi's sons into custody. However, the whereabouts of Gaddafi, who vowed to fight to the last drop of blood, is still unknown.