This follows Monday's parliamentary vote of no-confidence which ousted Manasseh Sogavare as prime minister.
A notice has been issued by the Acting Governor General for parliament to convene next week.
Ajilon Nasiu said nominations must be made by 4:00pm this Friday.
Meanwhile, two main groups lobbying to form the new government have set up camps in Honiara hotels ahead of the vote.
Mr Sogavare's group, which lost the no-confidence vote by 27 votes to 23 in the 50-seat parliament, is now claiming to have a majority again.