Malaysia's incumbent prime minister, Najib Razak, has conceded defeat following a historic election in which the ruling party was ousted for the first time in 60 years.
Speaking in a televised press conference on Thursday morning, Mr Najib said: "I and my colleagues accept the verdict of the people."
He said the National Front, which has ruled the country for almost the entirety of its modern-day history, "will honour the principle of democracy in the parliament".
Mahathir Mohamad, the country's 92-year-old former authoritarian ruler, said he expected to be named prime minister after leading an opposition alliance to victory.
As no individual party carried the 112 seats needed to lead on its own, Malaysia's king will be called upon to propose the new leader. But Mr Mahathir said he had won a clear mandate to form a new government and brushed aside any doubts that he would be the one to take the country forward.
"There is an urgency here, we need to form the government now, today," Mr Mahathir told a news conference, where he insisted that he would be sworn in as prime minister later on Thursday.
An official from the opposition alliance, known as the Pakatan Harapan (Alliance of Hope), said Mr Mahathir had been granted a meeting with the king at 5pm local time.
Pakatan Harapan comfortably beat Mr Najib's Barisan Nasional (National Front) coalition, and official results showed it took 113 seats - one more than the number required for a majority in the 222-member parliament.
But doubts remained over Mr Mahathir's status, Malaysian media reported, as Pakatan Harapan was not formally registered as a coalition prior to the vote.
Asked why he had not yet been sworn in on Thursday afternoon, Mr Mahathir said he "got up late" after the vote count went long into the night.
Mr Mahathir led Malaysia for 22 years until 2003, but returned from political "retirement" to take charge of the opposition, with Mr Najib embroiled in a corruption scandal and facing growing unpopularity towards a controversial new sales tax.
Looking downcast as he took to the stage to address the media alongside other senior National Front politicians, Mr Najib said: "The National Front will respect whatever decision is made by the king. I urge all Malaysians to be calm and to trust the king's wisdom to make the best choice."
Supporters of the incoming government took to the streets of Kuala Lumpur to celebrate their unexpected victory.
People stood on roadsides waving the white, blue and red flag of the opposition alliance that triumphed in Wednesday's election, while cars honked their horns as they sped past.
"I'm so happy," said Zarini Najibuddin while waving the opposition flag. "I hope we'll have a better Malaysia now. Malaysia reborn!"
Mr Mahathir was credited with modernising Malaysia during his 22-year rule that ended in 2003 but was also known as a heavy-handed leader who imprisoned opponents and subjugated the courts.
Additional reporting by AP
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