The government has been in an impasse since March, when it was hit by mass cabinet resignations and the exit of two coalition partners.
The defections led the opposition to claim the government had lost its majority in parliament.
Manele has since avoided a vote of confidence, which would eject him and his government from power if he loses.
The High Court ruled last month that the prime minister should recall parliament or resign, after he continued to avoid a no-confidence motion lodged by the opposition coalition.
On Friday, the appeal court said Manele must take steps before noon on Tuesday to facilitate convening parliament so lawmakers sit by May 7.
“The continued failure to take steps to facilitate the convening of parliament is inconsistent with the constitution,” it said in the judgement.
It dismissed Manele’s argument that the High Court had exceeded its powers.
“The court does not intrude on parliament by ensuring parliament can sit,” the court said.
Outside court, Attorney General John Muria said he was disappointed “but the court has spoken”.
The Royal Solomon Islands Police Force deployed officers outside the court and called for calm.
Commissioner of Police Ian Vaevaso, sworn in by Manele on Wednesday, had earlier issued a statement saying “police are independent of politics” and would not take sides.
A no-confidence motion against Manele was filed in March after 12 cabinet ministers resigned from his government and two parties quit the governing coalition.
The new opposition coalition of six political parties says that it commanded 27 seats compared to the government’s 23 seats.
Following the resignations, Manele appointed former leader and staunch Beijing ally Manasseh Sogavare as deputy prime minister, deepening the turmoil.
Chief Justice Albert Palmer in April ruled the country was at a “constitutional impasse”. (AFP)
