UPDATE 5-Sri Lanka's Rajapaksa ousted, ally nominated as successor

* Parliamentary speaker accepts president's resignation

* Exit follows popular uprising over economic meltdown

* Rajapaksa brothers barred from leaving country for 2 weeks

* Parliament to hold presidential vote on July 20

* Acting leader pledges more powers for parliament (Adds quote from protester)

By Uditha Jayasinghe, Alasdair Pal and Devjyot Ghoshal

COLOMBO, July 15 (Reuters) - Sri Lanka's parliament accepted the resignation of President Gotabaya Rajapaksa on Friday after he fled the country, paving the way for lawmakers to start repairing the island's shattered politics and resume efforts to ease its economic crisis.

After suffering from crippling shortages of petrol and diesel and runaway prices of basic items like vegetables and bread for months under the rule of Rajapaksa and his brothers, Sri Lankans are now waiting for lawmakers to elect a new president on July 20.

Until then, Prime Minister Ranil Wickremesinghe will be the interim president although protesters want him gone too. His private residence was set ablaze by demonstrators last weekend and his office stormed this week.

Nevertheless, the ruling Sri Lanka Podujana Peramuna (SLPP) party on Friday nominated Wickremesinghe to take up the top job full-time.

"Ranil Wickremesinghe is not the change we have fought so hard for," said Wimal Jayasuriya, 43, a martial arts specialist who is on a hunger strike opposite the prime minister’s official residence that was also sacked by protesters.

"We will not allow him to be president. The SLPP parliamentarians should stand with the people and not allow Ranil Wickremesinghe to become president."

The speaker of parliament, Mahinda Yapa Abeywardena, said lawmakers would "constitutionally appoint a new president".

"It will happen quickly and successfully. I request everyone to support this process," said Abeywardena, who received Rajapaksa's resignation the previous night.

Rajapaksa landed in Singapore on Thursday, having fled to the Maldives early on Wednesday on a military jet along with his wife and two security guards. Protesters occupied his home and office last weekend after surging past armed guards.

Sri Lanka's top court on Friday barred two of his brothers, former Prime Minister Mahinda Rajapaksa and former Finance Minister Basil Rajapaksa, from leaving the country without permission until July 28, according to anti-corruption group Transparency International Sri Lanka.

The group approached the court seeking "action against persons responsible for the current economic crisis".