For the election, Mahathir linked with the opposition alliance which includes his former opponent, Anwar Ibrahim.
The announcement was potentially put forward by the decision of the new government to bar Najib and his wife from leaving the country pending investigation of alleged corruption.
This means Mr Anwar could be out of jail sooner than June 9, his scheduled release date.
"The (king) has indicated he is willing to pardon Datuk Sri Anwar immediately", Mahathir told a press conference, using a Malay honorific.
Mahathir said Friday he would begin the process of obtaining an immediate pardon for Anwar, who was imprisoned twice on charges widely believed to be fabricated by the National Front to crush the opposition.
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Bridget Welsh, a Southeast Asia expert at John Cabot University in Rome, said it was hugely ironic that Mahathir, who damaged Malaysia's democratic institutions with his strong-arm rule, has returned as its political savior. Without it, he would be banned from political life for five years. Anwar is in custody on charges of sodomy and corruption and can not take any office until he is pardoned and released.
It was not clear when Anwar, who is now in hospital for treatment to his shoulder, would be freed. Amnesty International said Malaysia's first-ever change in government is an opportunity to "eradicate repressive policies" and put human rights first.
Speaking at a news conference, Mahathir also said he would announce a 10-member cabinet on Saturday, including ministers for finance, defense and home affairs.
Although Mahatir also imprisoned Anwar in 1998 following a power struggle, the two have recently become allies, with Mahatir saying he plans to eventually step down and allow Anwar to become prime minister in his place.
He was spurred out of retirement by allegations that Najib oversaw the wide-scale looting of sovereign wealth fund 1MDB.
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Najib denies any wrongdoing.
When asked if the restrictions on Najib were due to 1MDB, Mahathir said: "There are a lot of complaints against him all of which have to be investigated. we find that some of the complaints are valid".
"He, in fact, has hidden evidence of wrongdoing and that is wrong in law", he said, adding his new government would target those linked to the old regime suspected of corruption. "I respect the order and will remain in the country with my family", he wrote in his latest Twitter post. The senior police officer only confirmed "family members" of Najib had stayed in the apartment complex when Reuters asked if Rosmah had stayed there.
Mahathir's alliance defeated Barisan in a stunning election upset on Wednesday, ousting the coalition that has ruled the nation for six decades since independence from Britain.
His comments, however, might raise eyebrows.
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"The Malaysian people were defrauded on an enormous scale", said the Federal Bureau of Investigation, or FBI, at the time.