Mohamed Ibrahim also said pro-Morsi sit-ins would "God willing, soon ... be dealt with" based on a decision by the prosecutor, who has been examining legal complaints by citizens about the protests that have blocked major Cairo thoroughfares.
"God willing, it will be broken up in a way that does not cause losses," he said referring to sit-ins that have lasted about a month. "But, God permitting, it must end. We hope that they come to their senses ... and join their political process."
"With regards to the timing ... to disperse the protesters, there is complete coordination between us and the armed forces," the minister told a news conference.
"There are still meetings going on to set the appropriate time to implement that plan according to the complaints submitted to the prosecutor on transgressions of the law by the protesters."
The minister, who accused the pro-Morsi camp of exaggerating the numbers killed in clashes, said security forces used teargas to disperse demonstrators on a bridge because of concerns they could cause the bridge to collapse by lighting vehicle tyres.
But he said the security forces had not used any live ammunition, but had instead suffered buckshot wounds and injuries from live rounds fired by protesters.
A Reuters witness, at a field hospital run by Morsi supporters, saw several demonstrators wounded by buckshot and with injuries medics said were caused by bullets.
The minister also said a decision on where to hold Morsi, whose current location has not been announced, would be up to the investigating judge. When pressed by journalists about where Morsi would be taken, he said "mostly likely to Torah" prison.
Torah, on the edge of Cairo, is the jail where Mubarak, his sons and members of the former president's cabinet have been held after they were detained in the wake of the uprising that erupted in January 2011.