An emergency summit of West African leaders has refused to recognise the new leadership of Togo, condemning the transfer of power as a coup.
Faure was named as president within hours of his father's death
Regional body Ecowas has threatened to impose sanctions unless Togo returns to its original constitution and starts planning presidential elections.
Faure Gnassingbe, the son of the late president, was installed as leader after the constitution was changed.
He has vowed to organise free and open elections as soon as possible.
Leaders from the 15-member Economic Community of West African States, meeting in Niger, decided the changes in Togo's constitution, aimed at legalising the military appointment of Mr Faure, did not disguise the fact that what had taken place was a coup.
"The heads of states strongly condemn the intervention of the military which resulted in the appointment as president of the son of the deceased president," the group said in a statement.
A high-level delegation plans to go to Togo's capital, Lome, by Friday to express their objections in person.
The African Union, whose chairman Nigerian President Olusegun Obasanjo led the Ecowas summit, has also said it would consider imposing sanctions on Togo unless it restores "constitutional legality".
Mr Faure, in his first address to the nation, has promised "free and transparent" elections "as soon as possible".
But the BBC's Andrew Simmons says that while he spoke of national assembly elections, Mr Faure did not make any reference to elections for the head of state.
Under the original constitution, presidential elections should be held within two months of a president's death.
However, a constitutional amendment passed on Sunday - the day after Gnassingbe Eyadema's death - allows Mr Faure to serve out his father's term as president until June 2008.
After negotiations with the European Union last year, the late president promised to hold legislative elections under reforms intended to level the electoral playing field.
The EU froze aid to Togo in 1993 over the country's lack of democracy and poor human rights record.
The opposition has rejected Mr Faure's offer of elections, demanding that he step down.
Meanwhile, the International Organisation of French-speaking countries has announced that it has suspended Togo's membership.