The National Coalition for Supporting Legitimacy has called on its supporters to rally every day during the next week to fail the referendum.
Voting on the newly-drafted constitution is expected to take place on 14 and 15 January inside Egypt.
"In the lives of nations, there are decisive days ... so march forward with your revolution as you hang on to peaceful, innovative resistance," the alliance said.
In a statement released today, the Islamist coalition, which backs former President Mohamed Mursi, urged the masses to rally all week long "in order to push the coup to the edge, the edge of the abyss beyond which there is no rise".
The voting process for Egyptian expatriates has already begun on Wednesday in various Egyptian consulates and embassies abroad.