Ravalomanana supporters cheer their leader
Mr Ravalomanana, who has been declared the winner of December's election following a recount, was planning to be sworn in on Friday.
A spokesman for Mr Ravalomanana said he would postpone the ceremony at the request of the Organisation of African Unity (OAU) - but added that Mr Ravalomanana was not giving up the presidency.
The incumbent President, Didier Ratsiraka, said before the recount that he would not accept the result, as he felt the judges carrying it out were biased.
A delegation from the Organisation of African Unity (OAU) was due in Madagascar on Wednesday, in an effort to defuse the power struggle.
The island has been split between supporters of the two rivals ever since Mr Ravalomanana declared himself president after elections in December.
Partition threat
The governors of four of the six provinces - who support Mr Ratsiraka - have announced plans to secede from the capital and form an independent confederation.
Fears of fresh violence rose on Tuesday, after another key bridge was blown up and a northern province declared independence.
The OAU, which has warned that the island risked sinking into further violence and even partition, had called for a referendum to choose between the two rivals.
On Tuesday unidentified saboteurs blew up the Andrainomaitso bridge, destroying a vital road link between the island state's capital Antananarivo - controlled by Mr Ravalomanana - and the south-eastern coast.
Supporters of Mr Ratsiraka had already destroyed four bridges on supply routes into the capital since Mr Ravalomanana declared himself president in February.
They have also mounted roadblocks in an attempt to starve the capital of vital goods.
Economic meltdown
The OAU team will start its mission in the port-city of Tamatave, Mr Ratsiraka's stronghold.
"The only way to avoid violence and partition in a country which has done very well economically is to hold a referendum," said OAU Secretary General Amara Essy.
About 35 people have died in violence since the political dispute began and the economy of the island has been crippled.
On Monday, the High Constitutional Court ruled that he had won the election against veteran leader Didier Ratsiraka, following a recount of the ballots.
The votes were re-examined as part of a deal to resolve the crisis.
According to the court, Mr Ravalomanana received 51.46% of the vote and Mr Ratsiraka 35.9%.
The announcement of Mr Ravalomanana's election was greeted by huge celebrations on the streets of Antananarivo, where he has his power-base.