Ranil Wickremesinghe made the comments -- his strongest yet directed at the head of state -- at the prime minister's official residence, which he has refused to vacate since his dismissal in October.
"The president has to appoint me prime minister as I command a majority in parliament," he said.
"I am telling the president not to act like Hitler who bypassed the constitution... We are not going to allow him to do that."
President Maithripala Sirisena sacked Wickremesinghe and replaced him with Mahinda Rajapakse, the larger-than-life former president credited with ending Sri Lanka's bloody civil war with Tamil separatists in 2009.
However, with Wickremesinghe's supporters still controlling a majority in parliament -- which has witnessed brawls between MPs in recent weeks -- Rajapakse has lost two votes of confidence.
On Monday the Court of Appeal denied Rajapakse the authority to act as prime minister and stripped his cabinet of their powers, giving Rajapakse until December 12 to prove his legitimacy and that of his government.
Sirisena, a former opponent of Rajapakse, told a group of legislators on Monday that he would not reinstate Wickremesinghe even if the latter had the support of all 225 members of the legislature.
Rajapakse's lawyers on Tuesday filed an appeal with the Court of Appeal, but it was not immediately taken up for hearing.
Rajapakse urged his supporters on Monday night to remain calm and join his struggle to press for a general election nearly two years ahead of schedule.
Sirisena meanwhile told minority Tamil legislators who held talks with him on Monday evening that he would resolve the political vacuum "within 24 hours". However, there were no signs of a settlement by Tuesday afternoon.
The Supreme Court this week is also expected to rule on whether Sirisena's decision to dissolve parliament in November -- a move already suspended by the court -- was constitutional.
'I am telling the president not to act like Hitler who bypassed the constitution... We are not going to allow him to do that' Ranil Wickremesinghe said.