"It hurts to leave the country for political reasons, but I will stay in touch," he said on Monday night. "Soon I will return with more strength and energy."

The departure of Bolivia's first indigenous president, one of a wave of leftists who dominated Latin America's politics at the start of the century, has failed to end weeks of violent protests about allegations of fraud at the October 20 re-election.

The 60-year-old former llama herder and coca leaf farmer was viewed by many as a champion of the poor who brought steady economic growth, but to others he was an autocrat who overstepped by defying a referendum on presidential term limits.

His government collapsed on Sunday after the Organization of American States (OAS) delivered a damning report into serious irregularities during the October vote, prompting ruling party allies to quit and the army to urge him to step down.

Mexico granted asylum to Morales, its government confirmed.

"We will immediately proceed to inform Bolivia's foreign ministry that under international law, it should offer safe conduct" to Morales, Mexico's Foreign Minister Marcelo Ebrard told reporters on Monday.

Foes celebrated Morales' departure but also moved swiftly to find a temporary successor before a presumed new election in the landlocked nation that is one of South America's poorest, dependent on farming and natural gas.

With Morales' deputy and many allies in government and parliament gone with him, opposition politician and Senate second vice-president Jeanine Anez flew into the capital La Paz saying she was willing to take control. She was later taken by the military to the legislative assembly.

"If I have the support of those who carried out this movement for freedom and democracy, I will take on the challenge, only to do what's necessary to call transparent elections," said Anez, who is constitutionally next in line to assume the presidency.

Speaking tearfully about the crisis, she said the Senate would look to hold a session on Tuesday and urged members of Morales' Movement for Socialism (MAS) party to attend to find a constitutional solution and interim president.

Morales's resignation still needs to be approved by the Legislative Assembly, convened by both chambers of Congress.

Australian Associated Press