The appeal was lodged by Tshisekedi’s primary rival in the race, Martin Fayulu, who came second in the official results.
Armed officers and police in riot gear patrolled the streets around the court building in the capital Kinshasa and carried out identity checks on anyone entering the premises.
Official results released last Thursday by the Independent National Election Commission (CENI) gave Tshisekedi 38.57 of the December 30 vote, against Fayulu’s 34.8 percent.
Emmanuel Ramazani Shadary, the candidate backed by outgoing president Joseph Kabila, came a distant third with 23.8 percent.
Fayulu says the results were an “electoral coup” that he alleges was forged in backroom dealings between Tshisekedi and Kabila, who has been in power since 2001.
The packed court began its hearings at 11:30 am (1030 GMT), two hours later than scheduled, with the public hearings also carried live on radio and television.
Fayulu claims that he garnered 61 percent of the ballots. In the few opinion polls conducted before the vote, he had been tipped as the clear favourite.
“What has been declared is anything but the true result that came out of the ballot boxes and was posted in front of the different voting bureaux,” Fayulu’s lawyer, Albert Fabrice Puela, told AFP.
– Pushing for a recount –
The country’s top court has eight days to rule on the matter from the date that Fayulu’s appeal was lodged, on January 11.
But its nine judges are not due to sit on Wednesday and Thursday, which are public holidays here.
The influential Roman Catholic Church, which says it deployed 40,000 observers to monitor the poll, has also dismissed the official outcome as not reflecting the true result.
While it has held back from saying who it thinks won, it has urged the UN Security Council to press CENI to publish a detailed tally of its count.
Fayulu’s lawyers want CENI’s official results declared invalid and a full recount.
At the same time, they want to avoid the whole vote being declared null and void as that would allow Kabila to stay in power until a fresh election is organised.
Tshisekedi’s party, the Union for Democracy and Social Progress (UDPS), has said it would accept a court ruling calling for a recount.
– Doubts about the court –
Meanwhile, Kabila claims his supporters won nearly 350 seats in the 500-seat National Assembly, which under the constitution would give his party the power to designate the country’s prime minister.
So even if the court confirms Tshisekedi as president his CACH coalition, which won 50 seats, would be forced into some kind of power-sharing deal with Kabila’s camp.
Both Fayulu and Tshisekedi have expressed scepticism at the result of the parliamentary election.
Many observers are sceptical about the independence of the Constitutional Court’s nine judges, in part because some of them are former Kabila allies.
The DRC’s political crisis erupted two years ago when Kabila refused to step down at the end of his constitutional term in office, sparking protests which were brutally repressed.
The vast, unstable country has never had a peaceful transition of power since gaining independence from Belgium in 1960.
It became a battlefield for two regional wars in 1996-97 and 1998-2003, and the last two presidential elections, in 2006 and 2011, were marked by bloody clashes.