Togo has drawn huge international criticism over the way Gnassingbe, 39, came to power. He agreed last week to hold presidential elections but has not yet bowed to pressure from world leaders to step aside ahead of any poll.
"If they are serious about elections in 60 days that means Faure will be both a player in the field and the referee," said one Western diplomat in Togo.
The return to the original text means elections must be held within 60 days of the death of a ruling president. The changes made after Gnassingbe Eyadema died earlier this month would have left his son in office unchallenged until at least 2008.
African leaders called the transfer of power a coup, and have imposed sanctions on Togo, saying that the pledge of presidential elections was not enough.
The United States, the United Nations and European officials have added their voices to the outcry, urging Togo to return to constitutional order.