"This decision has no legal basis, and a government built on this basis does not have legitimacy," former Foreign Minister Abdullah Abdullah told reporters.
On Monday, Karzai was named the election winner by the Independent Election Commission after it decided to cancel a planned Nov. 7 runoff vote in the wake of Abdullah's withdrawal.
Abdullah pulled out of the second round accusing the IEC and some government officials of bias in favor of Karzai.
The election held in August was marred by violence and widespread allegations of fraud, which delayed the announcement of the final results for more than two months.
The fraud was investigated by a U.N.-led body that eventually threw out nearly a third of Karzai's votes, forcing the runoff.
Karzai was first elected president in 2004 and his latest victory will give him another five-year term.
His government has often been accused of corruption and weak governance.
On Tuesday, in his first media address after he was declared winner, Karzai promised he will work harder to eradicate corruption.
Abdullah took swipe at him, saying, "A government authorized by an illegal body cannot fight corruption."
Karzai also said his next government will be a "national unity government" in which "all Afghans can take part in it," though he did not make clear whether he wants his rival Abdullah to join.
Abdullah, asked if he will remain in opposition and form a political party, said he will "act like a pressure group to bring changes" to the current situation.