The elderly leader, who is starting his second stint as premier after having previously been in office for two decades, arrived at the office of a foundation he runs in the administrative capital Putrajaya.
Escorted by police vehicles, he briefly rolled down the window of his black car to wave at waiting reporters. He was due to hold meetings with senior civil servants.
Mahathir stormed to an unlikely election victory at the head of an opposition alliance against the Barisan Nasional (BN) coalition and its corruption-mired leader Najib Razak, toppling the regime that had led Malaysia since independence from Britain in 1957.
Voters turned out en masse to oust Najib after he was accused of involvement in plundering billions of dollars from sovereign wealth fund 1MDB in a sophisticated fraud that is now being investigated in several countries. Both he and 1MDB deny any wrongdoing.
The 92-year-old Mahathir -- who was himself accused of ruling with an iron fist in his first stint as premier that ended in 2003 -- is now the world's oldest elected leader.
The stock market opened for the first time since Wednesday's polls but did not slide as heavily as had been anticipated after Mahathir sought in a weekend speech to calm investors. It initially lost 2.7 per cent but quickly won back ground and was down just 0.2 per cent about an hour after opening.
Local currency the ringgit slipped as much as 0.9 per cent against the US dollar. Stocks linked to the previous regime suffered, with low-cost carrier AirAsia dropping as much as 13 per cent.
The airline's boss, Tony Fernandes, apologised Sunday after offering a glowing endorsement of Najib days before the election, flying with him on an AirAsia plane painted in the blue colours of the leader's coalition.
Ooi Chin Hock, a dealer with SJ Securities, told AFP he believed the "government is supporting the stock market to make sure there is not too much volatility".
Still, it has not been all smooth sailing since the historic win, with concerns over the slow formation of the cabinet as different parties in the winning alliance jostle for positions.
Mahathir appointed three ministers at the weekend despite previously having said he would name 10 cabinet members.
Jailed politician Anwar Ibrahim, Mahathir's nemesis-turned-ally, issued a statement Sunday insisting his People's Justice Party (PKR) still supported the new premier after a senior figure from his party said the cabinet appointments were made without their consultation.
Anwar, in jail on sodomy charges his supporters say are trumped up, is expected to be freed on Tuesday.
James Chin, a Malaysia expert at the University of Tasmania, said some degree of arguing was normal.
"People are just positioning. Everybody is after the plum posts," he told AFP.
Mahathir also faced criticism for saying that a controversial law passed before the election that punishes "fake news" with up to six years in jail would be reviewed rather than revoked.
He announced Sunday that it would be given a clear definition but that there was a "limit" to press freedom, despite having pledged during the election campaign to abolish it.
The ragtag opposition alliance, which had been trying for decades to topple BN, finally found success after Mahathir joined forces with them.
Mahathir had crushed the opposition parties during his time in power but they found common cause in their determination to topple Najib as allegations mounted over 1MDB, and he became increasingly authoritarian.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)