Lopez Obrador, the former mayor of Mexico City, told a rally of thousands of supporters in the capital's main square: "We will never accept usurpation nor recognise a president-elect who is illegitimate."
Mexico's electoral court is almost certain to confirm the ruling party's Felipe Calderon as president this week, but Lopez Obrador insists that he was robbed in the July 2 election.
He said: "We are going for deep change, root change, because that is what Mexico needs. It is a radical transformation. We are going for the construction of a new country that is fair and honorable."
For more than a month, his leftist supporters have been protesting the election result by occupying the giant Zocalo square, the symbolic centre of power in Mexico since Aztec times. They have also taken over a long section of the main Reforma boulevard, paralysing the city centre and causing traffic chaos.
Lopez Obrador did not say how he plans to set up a parallel government but in the past he has said that his supporters could continue the current street protests for years if necessary. He has also promised to avoid violence.
"We will not only decide on our form of government ... but something very important will also be defined: the basic plan for the transformation of Mexico"
Andres Manuel Lopez Obrador,
State of the nation
Calderon, a former energy minister favoured by business leaders for his free-market policies, says the election was fair and fully expects to be declared president.
The court has already thrown out Lopez Obrador's allegations of massive fraud. However, it still has to give a final result, declare that the election was clean and name the winner.
Leftist lawmakers seized the podium in congress and refused to allow Vicente Fox, the outgoing president, to deliver his last state of the nation address on Friday night. He withdrew from Congress and made his speech on TV instead.
If Calderon is declared president, leftist deputies could repeat that tactic on December 1 when he would have to enter congress to don the presidential sash and give an acceptance speech to start his six-year term.
Lopez Obrador said he and his supporters would draw up a plan for a new nation at a convention in the Zocalo on September 16, Mexico's independence day.
Opposition supporters have
brought traffic to a standstill
He said: "We will not only decide on our form of government ... but something very important will also be defined: the basic plan for the transformation of Mexico."
Mexico's top electoral court must declare a new president by Wednesday. Its ruling cannot be appealed.
The initial result showed that Calderon, of the National Action Party, won by around 244,000 votes or just 0.58 of a percentage point.