"First thing tomorrow (Monday) morning, I will submit to the Congress my resignation as president of the republic so that Congress may consider it," Mesa said in a message from the presidential palace late on Sunday.
"I am not ready to prolong this shameful comedy we are in," he added, as coca growers blocked roads and tried to cut Bolivia's gas and electricity supplies for a fifth day.
On Saturday, Bolivia deployed the army's 9th Division and police to oilfields to stop protesters from taking over gas installations to demand a new law governing gas exploitation.
Shutting down operations
The superintendent of fossil fuels said the Chaco oil company had shut down gas pumping and liquefying operations in the Bulo Bulo field.
The operation feeds the Bulo Bulo electricity plant, which in turn supplies the national electricity grid. However, the superintendent said the electricity supply would not be cut.
For five days, protesters have
been on strike in El Alto
For five days, protesters have been on strike in El Alto, where the international airport serving La Paz is located. They have cut roads from La Paz to the interior of Bolivia and to Argentina, Chile and Peru, demanding the expulsion of Aguas de Illimani, a subsidiary of the French firm Suez Lyonnaise des Eaux.
Mesa came to power in October 2003, after president Gonzalo Sanchez de Lozada was toppled by street demonstrations, which killed as many as 80. Mesa, an intellectual and historian, was vice-president at the time.
Crowds rallied outside the presidential palace late on Sunday in a show of support for Mesa, who acknowledged them by appearing on a balcony and waving a Bolivian flag.
"Mesa, we love you. The people are with you"
Crowds outside the palace
"Mesa, we love you. The people are with you," chanted emotional crowds comprised largely of young people and women.
Leaders of the third and fourth largest factions in Congress - former president Jaime Paz Zamora and populist leader Manfred Reyes Villa - called for Mesa to remain in power.
But Mesa is locked in a dispute with top opposition leader Evo Morales, head of the coca growers and the Movement Toward Socialism, the country's second-largest force in Congress.
Morales has called for protests aimed at blocking highways and occupying electrical and gas sectors, saying the existing fossil fuel law would convert Bolivia "into a country controlled by the international community".