Vital Kamerhe, the candidate who took 7% of the vote, is leading the Supreme Court challenge.But his lawyers walked out of the session after the court rejected all of their preliminary objections.
Overnight, the US said the elections were "seriously flawed", as it called for a review of the process.
The results' credibility has also been criticised by the European Union and the Carter Center, but the African Union said the polls were a success.
Mr Kamerhe, once an ally of Mr Kabila , broke away from the president's party to form the Union for the Congolese Nation (UNC). He comes from the Kivu region in eastern DR Congo, where Mr Kabila also draws much of his support. On the steps of the courthouse in the capital, Kinshasa, Mr Kamerhe explained why his legal team had walked out of the hearing after one hour.
The BBC's Thomas Hubert in Kinshasa says police in riot gear and armoured trucks were on guard nearby.
"We did not pull out of the legal case, but we refused to validate a parody of justice," Mr Kamerhe said.
Our reporter says that as soon as the opposition's 23 lawyers had left, the court resumed the hearing with those representing the electoral commission and President Kabila.
It must decide by 17 December whether or not to validate provisional results.
Without a legal team to support the opposition challenge, the Supreme Court is now expected to confirm President Kabila's re-election, our reporter says. Mr Tshisekedi has not mounted a legal challenge. He has rejected the result outright and has declared himself president. A recently formed national mediation committee – including religious and academic leaders – went to meet Mr Tshisekedi on Thursday.
But a spokesman for Mr Tshisekedi said he would not consider any other option than the recognition of what he regards as his electoral victory. President Kabila has rejected claims that he won elections through widespread rigging but admitted that "mistakes" had been made.
The AU and several regional bodies – including the Southern African Development Community – said the polls had been "successful" and disputes should be resolved through legal means.
In a statement earlier this week, the Carter Center, which had 26 teams of observers monitoring the elections, pointed to differences in the vote count between areas where Mr Kabila had strong support and areas that favoured Mr Tshisekedi.
Some constituencies in Katanga province "reported impossibly high rates of 99 to 100% voter turnout with all, or nearly all, votes going to incumbent President Joseph Kabila", the Center said. Meanwhile in Kinshasa, where Mr Tshisekedi has strong support, results from nearly 2,000 polling station stations were lost – roughly a fifth of the city's total. The elections are the first Congolese-organised polls since the end of a devastating war in 2003 which left millions dead. An earlier poll in 2006 was organised under the auspices of the United Nations.
Mr Kabila has been president since 2001 following the assassination of his father, Laurent and he is due to be sworn in on 20 December for his second term if his victory is confirmed by the Supreme Court.
Inside DR Congo
The Democratic Republic of Congo covers 2,344,858 square km of land in the centre of Africa, making it the 12th largest country in the world.