This follows Bushiri and his wife's re-arrest after they jumped bail in South Africa where they are wanted to face $6.6m fraud allegations.
"As a member of Interpol, Malawian police authorities now have an obligation to hand the two fugitives over to the global agency and South African authorities", said DA MP Angel Khanyile.
Khumbo Soko, one of the presidential elections case lawyers, has said today that he has stopped representing the Bushiri couple who are seeking bail following their arrest on Wednesday.
Bushiri's spokesman, Ephraim Nyondo, denied the couple's arrest was sparked by the warrant.
Meanwhile, the rights group Malawi Black Economic Empowerment Movement said Wednesday that Malawi should not extradite Bushiri and his wife back to South Africa unless the government ensures they will receive a fair trial.
It has been days since the pair fled South Africa undetected in contravention of strict bail conditions.
The official opposition Democratic Alliance (DA) has called on Interpol as well as South African and Malawian authorities to facilitate a smooth extradition process for the Busharis.
Bushiri is a self-proclaimed prophet and leader of his Enlightened Christian Gathering Church, which claims over 70 branches worldwide.
Bushiri tell Zimbabwe politician Kembo Mohadi say im go get "di crown" before dem name am vice-president, according to New Zimbabwe.
Ramaphosa said he was expecting a "detailed report on the whole Bushiri saga ... then we'll see what action needs to be taken because it should never have happened the way it did".
"We are going to take action, that's for sure", he said.
The mogul has huge investments in mining, telecommunications and the hospitality industry.