"The problem in Peru is there is political intervention in the organisation of football," Blatter told a news conference in Chile.
"On Monday we at FIFA need to receive an official document in which the government ... and the football federation ... agree to solve the problem in a period of 10 days.
"If we do not have this document by Monday the Peruvian federation will be suspended immediately."
Peru has already been stripped of the right to host next year's South American under-20 championship because of the row in which the government's Institute of Sports (IPD) is refusing to recognise Manuel Burga as FPF president.
TEAM'S FAILINGS
The dispute has caused an outcry in the country where the public and media are already exasperated at the failings of the national team.
One of South America's strongest sides in the 1970s and early 1980s, Peru have not reached the World Cup finals since 1982 and are bottom of the 2010 qualifying group.
If Peru are suspended by world soccer's ruling body FIFA the national team will be kicked out of the World Cup qualifiers and their clubs will not be able to take part in the South American Libertadores Cup.
"They will be suspended from all international activities," said Blatter.
He added a FIFA delegation visited Peru one month ago but was not received by the government nor the football federation.
"This situation hurts me," said Blatter. "It always hurts when FIFA has to intervene because of political actions in the organisation of football."
