"I am now considering myself as the only legitimate president of the Democratic Republic of Congo," Fayulu said in a statement. "As such, I urge the Congolese people not to recognize any individual who illegitimately claims that authority, nor obey any order emanating from such a person."
Fayulu suffered defeat earlier this month when Congo's election commission announced that another opposition leader, Felix Tshisekedi, had won the December 30 vote.
The former oil chief was expected to win the election, which was seen as a test of whether the country in Central Africa could turn into a democracy.
Fayulu calls for "peaceful demonstrations"
Fayulu accused Tshisekedi of conspiring with outgoing President Joseph Kabila to influence the votes "against the will of the Congolese people."
With the decision to keep the election of Tshisekedi, the constitutional court confirmed that "it is at the service of an individual and a dictatorial regime that does not respect the laws of the republic nor the most elementary rules of democracy and morals," said Fayulu. in a statement.
Fayulu claims to have won more than 60 percent of the vote in an "overwhelming victory", which he said was confirmed by editors and observers.
"It is nothing more than a constitutional coup since (court) installs an unelected individual in the highest office," Fayulu said in a statement.
He urged the international community not to recognize the results and urged the Congolese people to "take their fate in their hands by organizing peaceful demonstrations across the country" to defend the Constitution.
African Union questions election results
Meanwhile, the Southern African Development Community (SADC) urged the international community to respect the autonomy of the country.
Democracy in the DRC
The December vote was to elect a successor to Kabila, who has held the presidency since 2001.
Twenty-one candidates, including former Kabila Interior Minister Emmanuel Ramazani Shadary, entered the presidential race.
Of the opposition candidates, only Fayulu and Tshisekedi were considered with a serious chance to defeat Shadary.
If considered legitimate, the election would be the first democratic transition of power in the country since it became independent of Belgium in 1960.
CNN's Hamn Alkshali, Stephanie Busari and Bukola Adebayo contributed to this report.