Rajapaksa submitted his resignation Thursday, but the parliament speaker's office said they were checking the legality of the resignation before it is accepted.
Addressing a press conference, Abeywardene said Rajapaksa officially resigned from his position on July 14 and it has been accepted.
The speaker also said that Prime Minister Ranil Wickremesinghe will function as the acting president until a new president is elected in seven days.
Rajapaksa had fled to the Maldives and then to Singapore on Wednesday in the wake of a worsening economic crisis in the island nation. He appointed Wickremesinghe on Wednesday to "exercise, perform & discharge the powers, duties & functions of the Office of President with effect from July 13, 2022."
The Singapore Foreign Ministry said Thursday that Rajapaksa had arrived in the country for "a private visit." The ministry said he "has not asked for asylum and neither has he been granted any asylum. Singapore generally does not grant requests for asylum."
A statement issued by the Maldives government Thursday said that at the official request of the Sri Lankan government, diplomatic clearance for a Sri Lanka Air Force aircraft carrying Rajapaksa and his spouse on a transit visit was granted to land on July 13.
Amid mass protests, Abeywardene said last Saturday that the president would resign on July 13.
The development came after thousands of protesters stormed the presidential palace in the capital Colombo and set fire to the prime minister's home.
Protesters have blamed Rajapaksa's political dynasty for the crisis. Mahinda Rajapaksa, a brother to the president, resigned as prime minister in May.
Crippled by a shortage of foreign exchange reserves after the collapse of its tourism-dependent economy, the island nation of 22 million people has defaulted on all of its foreign debt.
It has been unable to pay for fuel and other essentials, resulting in anti-government protests. A lack of fuel to run power stations has in turn led to daily power cuts. Schools have been closed and state employees have been asked to work from home.
The government is negotiating with the International Monetary Fund (IMF) for a bailout package.
Months of protests have demanded Rajapaksa’s resignation.