Three people were killed in weekend clashes with the police.
General Miguel Vasquez, the police chief, initially claimed the protesters lynched a policeman, but reissued a statement on Tuesday, saying that the officer was found alive, though in shock.
The violence prompted the authorities to withdraw Sucre's 700 police officers on Sunday.
Citizen groups were left to patrol the city's streets until Tuesday, when Morales ordered the police to return.
The opposition-run provinces contribute about 80 per cent of Bolivia's national income.
Ruben Costas, the Santa Cruz governor and a leading opposition figure, said moves were under way to file a lawsuit against the military and police bosses for their role in what he called "the Sucre massacre".
On Tuesday, dozens of reporters demonstrated in Sucre's main square to protest against attacks on journalists.
Dozens of journalists were attacked by the police during the weekend clashes while unknown attackers also fired gunshots on a television station based in the troubled city.
On Monday, Ban Ki-moon, the UN secretary-general, and the US administration appealed for calm following the weekend violence.
The rewriting of the constitution is seen by Morales as a cornerstone of his reform agenda.
He says it will give the indigenous majority greater political powers.