In fact, he said he expects to be sworn in as prime minister today, and his coalition will have the support of 135 members of the 222-seat parliament.
"There has been some delays over a lack of understanding of the constitution, but we'd like to make it clear that there is an urgency here: We need to form the government now — today," Mahathir said. "That is because currently there is no government of Malaysia."
That statement follows tepid comments from sitting Prime Minister Najib Razak, who said earlier Thursday he accepted the verdict of the vote, but noted no individual party had achieved a simple majority, so it will fall to the country's king to decide who would be appointed the next prime minister.
"I accept, and my friends also accept, the verdict that has been delivered by the people," he said, according to a translation of the address, noting that his coalition was committed to respecting the principles of democratic parliament. "And because no party has gotten a simple majority, therefore the king will be making a decision as to who will be the prime minister," he added.
Mahathir is expected to replace Najib, and he was set to be sworn in as the world's oldest elected leader after his opposition alliance pulled off a stunning election win, ending six decades of rule by a coalition he had once led.
"Najib's role as an interim government is now over," Mahathir declared on Thursday, noting that "if the government is not appointed immediately, the country will be ... without a government."
Various news outlets cited official sources saying there would not be a swearing in of a new prime minister on Thursday, but Mahathir was resistant to that schedule.
"We hope that by 5 o'clock today we will have a prime minister," he said. "Any delay will mean that we will have no government. And when you say you have no government, you have no law, you have no constitution, and you don't have all those institutions which are created to give form to the government of this country."
"We need to have this government today, without delay," he added.
The 92-year-old led an opposition coalition to an unexpected victory over Najib, whose popularity had declined over rising living costs and in the wake of a multi-billion-dollar graft scandal at 1Malaysia Development Berhad (1MDB).
Mahathir led the Southeast Asian nation for 22 years and his unexpected return to the prime ministership ends the previously unbroken rule of Barisan Nasional (BN), the coalition that had
governed Malaysia since independence from Britain in 1957.
The stunning election outcome was expected to ruffle financial markets that were expecting a comfortable win for Najib and the BN.
The national stock market was set to be closed on Thursday and Friday after Mahathir declared a public holiday, but the ringgit currency weakened in offshore trading.
—Reuters contributed to this report.