"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.
Mesa said he had decided to submit his resignation "for the consideration of the country, for the consideration of you".
The president came to power in October 2003, after Gonzalo Sanchez de Lozada was toppled by street demonstrations that killed as many as 80 people.
An intellectual and historian, Mesa was vice-president then and has attempted to resolve differences between demands of business and agricultural workers and labour unions since taking the top office.
However, he said the crisis continues and he would resign as a result.
On Saturday, Bolivia deployed the army's 9th Division and police to oilfields to stop union protesters who were attempting to occupy the oilfields to demand a new law governing gas exploitation.
The superintendent of fossil fuels said the Chaco oil company had shut down gas pumping and liquefying operations in the Bulo Bulo field.
"First thing tomorrow (Monday) morning, I will submit to the Congress my resignation as president of the republic so that Congress may consider it... I am not ready to prolong this shameful comedy we are in"
Bolivian President Carlos Mesa
The operation feeds the Bulo Bulo electricity plant, which in turn supplies the national electricity grid.
However, the superintendent said that electricity supply would not be cut.
Meanwhile, coca growers also cut a major highway between Cochabamba and Santa Cruz, who are part of the protests in Bulo Bulo.
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.
The coca growers also tried to occupy other electrical plants in an attempt to pressure Congress to demand larger royalties from petroleum companies.
Business leaders in Santa Cruz province have demanded autonomy, while growers of coca, from which cocaine is extracted, joined with labour unions in opposing economic measures they say impact them unfairly.
For five days, protesters have
been on strike in El Alto
Among the measures was Sanchez de Lozada's plan to sell Bolivia's natural gas, one of the largest reserves in South America, to the United States.
The plan to build a $5-billion pipeline through Chile, an old foe of Bolivia, sparked a nationalist backlash in 2003, leading to his ouster.
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," chanted emotional crowds comprised largely of young people and women.
"Mesa, we love you. The people are with you"
Crowds outside the palace
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.