The American Embassy in Cairo will close to the public on 30 June "in anticipation of demonstrations that may turn violent."
The embassy warned its personnel against attending anti-government protests on 30 June and said potentially violent protest activity may occur before 30 June.
Americans were advised to "maintain a low profile and restrict movement" to their immediate areas from 28 June.
The opposition Rebel campaign has stressed its commitment to peaceful protests. However, the US Embassy warned that "even demonstrations or events intended to be peaceful can turn confrontational and possibly escalate into violence."
Other countries, including France and the UK, have warned their citizens to avoid large gatherings on 30 June.
Rebel is a campaign to collect 15 million signatures calling for Morsi's removal and early presidential elections.
The campaign, which is supported by the opposition National Salvation Front (NSF), argues that Morsi, who hails from the Muslim Brotherhood, has failed to make any progress since coming to power.
Rebel announced recently that it had collected more than 15 million signatures.
The Muslim Brotherhood has said calls for snap elections are 'unconstitutional' and an obstacle to true democracy.