Mansour, who took oath as head of the Supreme Constitutional Court (SCC) earlier in the day, said fresh elections were "the only way" forward. But he gave no indication of when they would be held, BBC reported.
Morsi, the country's first freely-elected leader, described the political developments as a military coup. The army, though, said Morsi had "failed to meet the demands of the people".
The late Wednesday developments occurred after days of mass rallies against the Islamist president.
Protesters accused Morsi and his party, Muslim Brotherhood, of carrying out an Islamist agenda and failing to tackle Egypt's economic problems.
At least 10 people were killed and scores injured in clashes across the country. Some 50 people have died since the latest unrest began Sunday, according to the health ministry.