Egypt's army-installed government on Saturday promised supporters of ousted President Mohamed Mursi a safe exit from their protest camps and urged them to rejoin the political process.
"Your continued sit-ins have no legal or political use. You have a safe exit, you will be politically integrated," Latif said in an announcement on state television.
Thousands of Mursi supporters have gathered in two camps in the capital to demand the reinstatement of Mursi, an Islamist from the Muslim Brotherhood who was overthrown a month ago to the day.
The military had threatened to remove them by force. But on Friday, following appeals form religious leaders as well as foreign governments to avoid a bloodbath, the interim government said it would blockade the camps but not storm them.
"If you think you're upholding the Muslim Brotherhood, your safe exit from the squares will allow the group to return to its role within the democratic political process," Latif said.
"If you think you're protecting yourself by staying with your colleagues, we pledge your safe and secure return to normal life as a free and honest citizen."
Latif said many people wanted to leave but they faced threats from the protest leaders. Anyone involved in crimes, including torture, killing and kidnapping, would face prosecution, he said.
"You are brain-washed, subject to psychological manipulation. You are being used as a political-bargaining chip," he said, directing his comments to the demonstrators.
Mursi became Egypt's first freely elected president in June 2012, 16 months after a popular uprising toppled long-ruling strongman Hosni Mubarak. He was himself ousted on July 3 after weeks of demonstrations against his rule.
Almost 300 people have died in political violence since then, including 80 of his supporters killed by security forces in clashes on July 27. Mursi is now in custody at a secret location.