[Nada que destacar de la protesta ciudadana, todavía]
The left-winger said the country's highest electoral tribunal made an illegitimate decision.
Mr Lopez Obrador had accused winner Enrique Pena Nieto of using illicit money to buy votes and media coverage.
"I cannot accept the ruling of the electoral tribunal, which declared the presidential election valid," Mr Lopez Obrador told reporters on Friday - just hours after the court's decision.
"The elections were neither clean nor free or genuine, therefore I will not recognise an illegitimate administration that emerged from votes that were bought and other grave violations of the constitution."
The former Mexico City mayor also called on his supporters to hold a demonstration in the capital's main square on 9 September.
Six years ago, after losing the presidential election by a narrow margin, Mr Lopez Obrador led weeks of protests that caused disruption in central areas of the capital.
On Thursday, all seven judges on the Federal Electoral Tribunal voted to reject the runner-up's accusations.
"There is no proof of vote-buying, there is no proof of coercion," Judge Flavio Galvan Rivera told the tribunal.
Mr Pena Nieto's Institutional Revolutionary Party (PRI), which governed Mexico for 71 years until 2000, denied any wrongdoing.
A recount of the election result gave Mr Pena Nieto 38% of the vote to Mr Lopez Obrador's 31%.
The BBC's Will Grant, in Mexico says that it is now clear that Mr Pena Nieto will be sworn in as Mexico's next president on 1 December.
"It is time to start a new phase of work on Mexico's behalf," Mr Pena Nieto tweeted after the ruling.
The decision sparked minor clashes between police and demonstrators
"With dialogue, understanding and agreements, we move together for the unity and greatness of Mexico."
There were minor scuffles between police and anti-PRI protesters outside the court after the decision was announced on Thursday.
A student movement has organised several demonstrations against Mr Pena Nieto's victory since the election.
But there are very few options left for Mr Lopez Obrador and his supporters, and the tribunal's decision - while expected by many - may have taken the wind out of their sails, our correspondent adds.
Mr Lopez Obrador, who leads the Party of the Democratic Revolution (PRD), accused the PRI of bribing voters with presents ranging from supermarket gift cards to fertiliser, cement and livestock.
He also claimed Mr Pena Nieto had broken campaign rules by overspending, and that Mexico's media was biased in favour of the PRI candidate.
One of the main challenges awaiting the new president will be the future of current government anti-drugs policy.
The PRI did not win a majority in congressional elections, also held on 1 July. This means he will probably need support from opposition parties.
Nota de BBC News: http://www.bbc.co.uk/news/world-latin-america-19440654