Democratic Republic of Congo opposition leader Etienne Tshisekedi has called on the security forces to stop obeying orders from President Joseph Kabila.
Mr Tshisekedi made the call after rejecting Mr Kabila's victory in last month's disputed elections.
Mr Kabila, 40, is due to be sworn in on Tuesday, while Mr Tshisekedi, 79, has planned his own inauguration for Friday.
An aide of Mr Kabila said Mr Tshisekedi was following a "criminal logic".
Many observers have criticised the polls as seriously flawed.
The elections were the first Congolese-organised polls since the end of a devastating war in 2003 which left some four million people dead.
Rival government
On Friday, the Supreme Court confirmed official results showing that Mr Kabila won with 49% of the vote against 32% for Mr Tshisekedi.
But Mr Tshisekedi said he rejected the results and was now the president.
"I will be sworn in next Friday before the Congolese people gathered at the Martyrs' stadium," he said.
Mr Tshisekedi said he was offering a reward for the capture of Mr Kabila and had dismissed his government.
He also called on the security forces and civil servants to disobey Mr Kabila's orders.
"I'm calling on you to only obey the legitimate authority voted in by the people, not individual adventurists who will have to answer before the Congolese and international judiciaries."
A senior member of Kabila's campaign team, Aubin Minaku, warned that Mr Tshisekedi could be arrested for trying to form a rival administration.
"Mr Tshisekedi is following a criminal logic," he said.
"Anywhere in the world, when an individual commits a crime, whatever his rank, even a presidential candidate, especially when he incites international crimes, the state must react vigorously, and the International Criminal Court should react vigorously too."
Mr Tshisekedi led the campaign for democracy under former leader Mobutu Sese Seko but these were the first elections he has contested.
He boycotted the last poll in 2006, organised under the auspices of the United Nations, after claiming they had been rigged in advance.
Mr Kabila has been president since 2001 following the assassination of his father, Laurent and he is due to be sworn in on Tuesday for his second term.
Last week, Mr Kabila admitted there had been mistakes in the election process.
But he rejected concerns that the results lacked credibility.
The US-based Carter Center, which sent observers to the election, said the vote was too flawed to be credible.
The US state department called for a review of irregularities and the EU described parts of the election process as "chaotic".
However, the African Union described the elections as a success.
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