Mexican President Vicente Fox has promised that the 2 July presidential poll will be Mexico's "cleanest ever".
Lopez Obrador is known for his fiery speeches
In a TV address, Mr Fox said his administration would stop showing adverts to promote its public works and social programmes until after the vote.
Opposition candidates accuse Mr Fox, who is barred from standing, of using his office to influence the election.
Candidate Andres Manuel Lopez Obrador has apologised for calling Mr Fox names but again accused him of interference.
In a public letter to Mr Fox, Mr Lopez Obrador said he regretted some of the personal attacks in his election campaign.
He said he had made a mistake by telling the president to "shut up" and calling him a "chachalaca," a notoriously noisy bird.
But in his letter, Mr Lopez Obrador, the candidate of the leftist Party of the Democratic Revolution (PRD), also accused Mr Fox of "verbal incontinence".
He said Mr Fox was breaking election law by promoting Felipe Calderon, who is running as the candidate of Mr Fox's National Action party (PAN).
Mexican presidents, who just serve one six-year term, are forbidden by law from trying to influence elections.
As well as Mr Lopez Obrador, Roberto Madrazo of the PRI, the Institutional Revolutionary Party, has accused the president of interference.
Mr Fox's spokesman Ruben Aguilar said those accusing the president of meddling were trying to "destabilise the electoral process" and "were traitors to democracy and the Mexican people".
Calderon (centre) is now in the lead, opinion polls suggest
Mr Fox has denied he is trying to boost Mr Calderon's campaign.
In a national address on Monday night, the president said he would stop recording radio and television commercials promoting his administrations achievements in line with an agreement with the federal electoral authorities.
"I will do everything in my power to make sure the results of the election faithfully reflect the political will of the majority of Mexicans," he said.
Correspondents say the latest arguments may set the tone for the coming weeks as the election heats up into a race between Mr Calderon and Mr Lopez Obrador.
Opinion polls suggest Mr Calderon has now overtaken Mr Lopez Obrador who had been seen as the front runner for several months.