A royal pardon would reverse Anwar's conviction and make him eligible to actively participate in politics.
Mahathir was spurred out of retirement by a corruption scandal at 1MDB, a state fund that is being investigated by the US and several other countries after associates of defeated Prime Minister Najib Razak allegedly stole and laundered $4.5 billion from it.
The pardons board in Malaysia's capital will meet on Wednesday to discuss Anwar's release and Mahathir said he would be released the same day.
"I'm not in a rush", Anwar was quoted as saying.
Cracks have already emerged, with officials from Anwar's party alleging that Mahathir bulldozed the announcement of three top Cabinet posts. He and his supporters say the charge was politically motivated.
During the campaign, Mahathir, who was prime minister for 22 years in a previous stint from 1981, promised to step aside and make Anwar prime minister, once he was pardoned. Anwar became Mahathir's heir apparent, but they fell out during the 1998 Asian financial crisis and Anwar was sacked.
Najib's Barisan Nasional (BN) coalition last week suffered a shock defeat to an alliance of parties headed by the elderly Mahathir Mohamad, ending the corruption-mired regime's six decades in power.
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In an astonishing U-turn past year, Anwar shook hands with Mahathir and agreed to join forces to oust scandal-tainted Najib.
1MDB is now under global probes in at least six countries, including Switzerland and Singapore, over charges of money laundering and bribery. He has also ordered the attorney general who cleared Najib of any wrongdoing in 2016 to go on leave pending an investigation, while the head of the anti-graft body has resigned. "That put us again under tremendous pressure", Fernandes said, adding that his airline had added 120 flights.
In his Tuesday remarks, Mahathir said whether Najib would serve time in jail would depend on the results of a probe into the scandal.
The Swiss attorney general's office said on Tuesday that federal prosecutors were seeking quick talks with Malaysian counterparts on how to press forward with the investigation.
He said that Anwar, a former enemy turned ally, may be just a member of parliament for a while.
Reuters reported that the Malaysian Anti-Corruption Commission found evidence in late 2015 that RM42mil was transferred from a former subsidiary of state fund into an account of Razak. The fund was set up by Najib in 2009 to promote economic development but accumulated billions in debt.
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.