Sri Lanka is in deep financial crisis and the crowds say they won't leave until both men quit their posts. The parliament Speaker had earlier said the president would resign on 13 July.
Mr Rajapaksa, whose whereabouts are unknown, has not spoken publicly since his residence was stormed on Saturday.
Sources have told the BBC he is on a navy vessel in Sri Lankan waters. He was moved to safety before protesters entered the presidential palace.
On Monday, Prime Minister Ranil Wickremesinghe's office said in a statement it had been informed by Mr Rajapaksa that he would step down on Wednesday.
But under Sri Lanka's constitution, his resignation can only formally be accepted when he resigns by letter to the Speaker - which has yet to happen.
Prime Minister Wickremesinghe had earlier also said he would step down from his position. His house was set on fire during Saturday's unrest (Source: BBC).