The Mexican Electoral Court is meeting to rule on an appeal against the result of the 1 July presidential election.
The centre-right candidate, Enrique Pena Nieto, was declared the winner after a recount of nearly half of the votes.
The runner-up, Andres Manuel Lopez Obrador, then lodged a complaint.
He accused his opponent of buying millions of votes and breaking the law by exceeding spending limits.
Mr Pena Nieto rejects all the charges.
After the recount, Mexican electoral authorities said Mr Pena Nieto had won 38.21% of the vote to Mr Lopez Obrador’s 31.59%.
But Mr Lopez Obrador, from the left-wing Party of the Democratic Revolution (PRD), says the vote should be declared void.
“Article 41 of the constitution, which states that elections must be free and fair, was violated,” he said.
The electoral court has until 6 September to issue a ruling, but analysts say it is expected to do so before the Congress reconvenes on Saturday.
The PRI, which governed Mexico for 71 years until 2000, has been the target of many protests organised by a new student movement – YoSoy132 – since the vote.
The students accuse the party of fraud and say the PRI candidate had unfair advantage during the campaign as he enjoyed favourable media coverage.
The new Mexican president is due to take office on 1 December.
One of the main challenges awaiting the new president will be the future of current government anti-drugs policy.
Since President Felipe Calderon deployed the army to fight Mexico’s powerful trafficking cartels in December 2006, more than 55,000 people have been killed in drug-related violence.
Mr Pena Nieto’s Institutional Revolutionary Party (PRI) did not win a majority in congressional elections, also held on 1 July.
This means he will probably need support from opposition parties to enact reforms in key sectors such as energy, tax and labour