Morales, speaking at an earlier news conference, tried to placate critics by saying he would replace the country's electoral body for the new vote, though his opponents - already angry that he ran in defiance of term limits - were not assuaged.
In a preliminary report issued late Saturday, the OAS said its team of 36 investigators determined that there were multiple issues with the election that President Evo Morales says gave him an unprecedented fourth term.
On Wednesday he flew to La Paz, Bolivia's capital, with a resignation letter for Mr Morales to sign and a bible "in order that God returns to the palace".
Morales declared himself the outright victor even before official results indicated he obtained just enough support to avoid a runoff with former President Carlos Mesa.
Morales, who came to power in 2006 as Bolivia's first indigenous leader, has defended his election win but has said he would adhere to the findings of the OAS audit.
U.S. Undersecretary of State for Western Hemisphere Affairs Michael Kozak echoed that view on Twitter: "Bolivian citizens deserve credible and transparent elections that they can trust to represent their will".
Morales said on national television he was stepping down "for the good of the country".
Mesa, who came in second in the October 20 election, joined former presidents Jaime Paz Zamora and Jorge Quiroga in urging the military not to put down the protests. Police retreated to their barracks in at least three cities, and there were reports that some in two cities were openly declaring mutinies.
The country's military chief called on Morales to resign earlier in the day after his reelection victory touched off weeks of fraud allegations and deadly violence.
In this case, and based on Article 169 of the Bolivian Constitution, the president of the Senate has to fill the position until new elections are held. "We are asking that both sides hear us", Sergio Rengel, a leader in the tourism sector, told The Associated Press.
Mesa rejected the suggestion to hold talks.
"The Right states Eva must resign.' I would like to inform you, brothers and sisters, to each one of Bolivia and the entire world, I won't resign", Morales, a socialist, stated in a public occasion.
Morales denounced the seizure of the media outlets.
He also called on the opposition to the negotiating table to find a negotiated solution to the crisis.