The former actor-comedian plans to contest in an MDP primary to seek re-election on the party's ticket.
A 13-year jail sentence handed to the former opposition leader was suspended for review.
The top court concluded a review of Sheikh Imran's terrorism conviction.
Bisham was accused of failing to perform her duties as an independent state official.
Ahmed Naseem previously served as foreign minister in former president Nasheed's cabinet.
Inquiry commissions were instituted by presidential decree hours after Solih took the oath of office.
The two-day festival began with water sports and is due to end with a football match between politicians.
The release of political prisoners on the first day in office was a campaign pledge of President Solih.
The new ambassador of the United States presented her letter of credence to the president.
Nazim said he facilitated a meeting between the MDP parliament leader and former president Gayoom's son.
There are 161 pledges covering 23 sectors.
Some appointments drew criticism over qualifications, allegations of corruption and potential conflicts of interest.
Solih took the oath office with thousands watching on at the national stadium in Malé.
More than 300 foreign dignitaries from 46 countries were expected to attend the inauguration ceremony.
Yameen said he was respecting the wishes of thousands of supporters.
The four leaders met for the first time since September's election victory.
Former speaker Shahid is expected to join the cabinet.
