A statement read on state TV said the council would rule until presidential and parliamentary elections are held within six months, the Los Angeles Times reported. The parliament was elected in a November vote widely seen as rigged.
Prime Minister Ahmed Shafiq, whose Cabinet is staying in place for the interim period, also appeared on TV to say the economy was "stable" and his caretaker government would work "to bring security back to the Egyptian citizen," The New York Times reported.
The traffic flow in Cairo's Tahrir Square resumed Sunday for the first time in weeks as the military removed tents, army officials said.
"We do not want any protesters to sit in the square after today," Mohammed Ibrahim Moustafa Ali, head of the military police, told protesters and reporters, Irish radio RTE reported.
Soldiers formed lines and moved in around the few protesters who remained in the square with some yelling "peacefully, peacefully," the radio reported.
Several hundred protesters are refusing to leave until the promises of reform are implemented and scuffles between soldiers and protesters briefly erupted, Channelnewsasia.com reported.
After 18 days of protests, shops and banks were expected to open in the Egyptian capital. CNN said the country's stock exchange was expected to be back in business Wednesday.
Tanks and troops guarding strategic buildings in the capital since the outbreak of protests remained in place, but police have disappeared from the streets, CNN said.
Egyptian blogger and Google executive Wael Ghanim -- whose Facebook page reportedly triggered the protests -- called on Egyptians to resume work and "work like never before and help Egypt become a developed country," CNN said.
Hours after former President Hosni Mubarak's resignation was announced and he and his family were reportedly whisked off to the resort of Sharm el-Sheik, Swiss authorities said they were freezing assets the family had in the country, the British daily The Telegraph reported.
Mubarak may have amassed a fortune of more than $4.8 billion although there are reports that it could be as much as $64 billion, The Telegraph said.