More than 40,000 opposition supporters demonstrated peacefully on Wednesday.
Rajoelina, whose private TV station was closed by the government in December, called on them to stage a general strike and accused the president of running Madagascar as a dictatorship.
Jean Ping, a diplomat for the African Union (AU) said he was "deeply concerned by the prevailing political tension and the risk it poses to the stability of the country".
He urged those involved to end the crisis through "dialogue and respect for constitutional order and legality".
The president has accused his rival of stirring tension in an effort to overthrow the government.
Both parties have called for calm but have yet to initiate talks to resolve the impasse.
The political crisis risks harming Madagascar's image as a popular tourist destination and dissuading foreign investors keen to exploit its reserves of oil and minerals.