WASHINGTON (Reuters) - President Barack Obama welcomed the declaration of liberation by Libya's new leaders Sunday and urged the transition government to respect human rights and work toward democracy after the fall of Muammar Gaddafi.

"After four decades of brutal dictatorship and eight months of deadly conflict, the Libyan people can now celebrate their freedom and the beginning of a new era of promise," Obama said in a written statement.

With the fighting over, Obama said Libya's Transitional National Council should turn its focus toward elections.

Obama has touted Gaddafi's death Thursday as the beginning of a new time for Libyans and as vindication of a cautious strategy in which the United States backed a NATO air campaign to help rebels but steered clear of a lead role.

Obama had been criticized by Republicans at home for what has been described as a "leading from behind" strategy.

Libya's new rulers, he said, should "continue living up to their commitments to respect human rights, begin a national reconciliation process, secure weapons and dangerous materials, and bring together armed groups under a unified civilian leadership."

The United States would cooperate with its international allies to "help advance a stable, democratic transition," Obama said.

(Writing by Caren Bohan; Editing by John O'Callaghan)