The incumbent leader said he accepted the verdict of the vote, and asserted that there had been no fraud in the election. Najib said no individual party had achieved a simple majority, so it will fall to the country's king to decide who will be appointed the next prime minister.
Najib said, however, that there will be change for the country, and he is committed to ensure a resolution.
"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.
That sentiment was not well received by Mahathir Mohamad, who led his opposition coalition to victory over Najib's coalition.
Speaking at a subsequent news conference, Mahathir said: "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.
Despite various news outlets citing official sources saying there would not be a swearing in of a new prime minister on Thursday, Mahathir was adamant that the king needed to appoint him to the role immediately.
"We hope that by 5 o'clock today we will have a prime minister," he said during his news conference.
If sworn in, Mahathir would be the world's oldest elected leader. Mahathir led the Southeast Asian nation for 22 years anda 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 will 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.