The Court of Appeal in an interim order Monday temporary halted Rajapaksa and his Cabinet from functioning in their positions in response to a case filed by 122 legislators against his disputed government. The court set the hearing of the case for December 12 and 13.
Rajapaksa had said on Monday that he would appeal against the Court of Appeal's interim order.
"We will not agree with the interim order issued by the Court of Appeal today suspending the Cabinet. We will appeal to the Supreme Court first thing tomorrow against it," Rajapaksa said in a statement.
He said that it was the Supreme Court which has the power to interpret the Constitution.
As many as 122 parliamentarians of Wickremesinghe's United National Party (UNP), Janatha Vimukthi Peramuna (JVP) and Tamil National Alliance last month filed a petition in the Court of Appeal challenging Rajapaksa's authority as the prime minister.
The interim ruling was a major blow to both President Maithripala Sirisena and Rajapaksa after the former had appointed his ex-rival as the prime minister on October 26, plunging the country into a major constitutional crisis.
Sirisena later dissolved Parliament, almost 20 months before its term was to end, and ordered a snap election. The Supreme Court overturned Sirisena's decision to dissolve Parliament and halted the preparations for snap polls.
The political crisis has crippled the government for more than a month.
Ousted prime minister Ranil Wickremesinghe and Rajapaksa both claim to be the prime ministers. Wickremesinghe says his dismissal is invalid because he still holds a majority in the 225-member Parliament.
Prior to the crisis, Wickramasinghe's UNP had the backing of 106 parliamentarians while Rajapaksa and Sirisena combine had 95 seats.
Rajapaksa has, so far, failed to prove his majority in Parliament.
Wickremesinghe, with the support from the main Tamil party, claims to have the support of more than 113 legislators, required for a simple majority.
The Tamil National Alliance (TNA) has 16 seats in the house and JVP has six legislators.
The UNF has moved three no trust motions against Rajapaksa, who has refused to step down.
The Sri Lankan president has said that due to sharp personal differences with Wickremesinghe he would not reappoint him as the Prime Minister.
However, Wickremesinghe's UNP claims that Sirisena will be left with no choice as he would be the man who will command the confidence in the House.
(With inputs from agencies.)