She said the full pardon for her father, who is now in a hospital recovering from shoulder surgery, was sought due to a "miscarriage of justice".
Mahathir also said he welcomed foreign direct investment in Malaysia by China and other countries, but such investment must bring in capital and technology and provide jobs for Malaysians.
Anwar's release paved the way for him to return to politics, following a surprising election victory last week by his opposition political coalition, including Anwar's former foe Mahathir Mohamad, who was sworn in Thursday as Malaysia's new prime minister.
In "an initial stage, maybe lasting one or two years, I will be the prime minister", Mahathir said, speaking by live video link from Kuala Lumpur to a Wall Street Journal CEO conference in Tokyo.
Their newfound alliance is a stunning turnaround from the 1990s when - on the orders of Dr Mahathir and his government - Mr Anwar was arrested and jailed on charges of corruption and sodomy.
The volatile relationship between Mahathir and Anwar has dominated Malaysia's political landscape for over three decades and is central to the future of the alliance.
Mahathir is also racing ahead with an investigation into graft at 1Malaysia Development Berhad (1MDB), a state fund founded by the ousted Najib that is sunk in a multi-billion-dollar graft scandal.
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Anwar, who was imprisoned at the Sungai Buloh Prison, was scheduled to be freed on June 8. "There will be no special powers given except as are given to ministers or deputy ministers or deputy prime ministers", he said.
Cracks have already emerged, with officials from Anwar's party alleging that Mahathir bulldozed the announcement of three top Cabinet posts.
In an astonishing U-turn past year, Anwar shook hands with Mahathir and agreed to join forces to oust scandal-tainted Najib. He and his supporters say the charge was politically motivated. Once a high flyer in the ruling party, Anwar was convicted of homosexual sodomy and corruption after a power struggle with Mahathir in 1998.
"Seeing him walk free makes me emotional, but the fight is not over", said Ridzuan Ismail, an Anwar supporter at the hospital.
Mahathir is the leader of the ruling alliance and Anwar's PKR won the majority of parliamentary seats in the group. In a statement Sunday, Anwar reiterated his party's support for Mahathir's leadership but called for decisions to be made jointly.
"I think we need to let Mahathir do his work to save Malaysia and to get back its system of government".
In the WSJ report published online Tuesday, Dr Mahathir reportedly said he would not offer Najib freedom in an effort to reclaim the missing funds.
The head of Malaysia's anti-corruption watchdog resigned on Monday, while attorney-general Mohamed Apandi Ali was put on leave as Mr Mahathir moved to step up the investigation into allegations of corruption at the 1MDB fund, which has attracted the attention of prosecutors and regulators around the world.