Both the opposition leaders have filed separate petitions in the matter in the High Court.
Chennithala, in his petition, filed with Kerala Chief Minister Pinarayi Vijayan and IT secretary M Shivasankar as respondents, said that the IT secretary is not authorised to sign such an agreement.
"The agreement was signed without the knowledge of the Cabinet or the government. It is a mystery that such an agreement was signed with the jurisdiction of the New York court. Therefore, it is urgent to stay the data collection of the company," the petition said.
"And the amount of compensation for patients must be billed from the Chief Minister and the IT Secretary. The court must intervene to ensure that this amount is transferred to COVID-19 patients," it added.
Surendran also sought a vigilance enquiry into the agreement in his petition.
"The Department of Health has had data of more than one crore people since 2014 as part of the e-Health programme. This must be protected and the agreement with the US company should be cancelled," his petition said.
A batch of petitions is already pending before the Kerala High Court in the matter.
( With inputs from ANI )