Mesa addressed his countrymen late Monday, hours after riot police fired tear gas to scatter demonstrators trying to lay siege to the Government Palace.
"This is as far as I go," he told them. "I have decided to present my resignation as president of the republic."
It was his second offer to step down in three months. Mesa also submitted his resignation during similar protests in March, arguing the country was becoming ungovernable. Lawmakers rejected his offer, essentially giving him a new mandate.
This time, too, he suggested he might leave the matter up to the legislature. Mesa said he would "continue to be president until Congress makes a decision about the future of the country."
"In a nation that boasts more coups than years as an independent republic, President Carlos Mesa's resignation is not surprising and is more likely this time to be accepted by the Bolivian Congress," said CBS News Foreign Affairs Analyst Pamela Falk. "Unlike former Bolivian presidents who have fled in small boats across Lake Titicaca, President Mesa is attempting to leave the country with a clean slate, allowing the legislature to chose a president who is perceived to be more responsive to the nation's poor."
Earlier Monday, tens of thousands of demonstrators, including indigenous women in black bowler hats and farmers in baseball caps, snaked down into the capital from hilltop slums to stage the largest demonstration in La Paz in weeks.
Disgruntled miners created thunderous booms by tossing dynamite sticks, and more than 500 protesters were turned away by acrid tear gas as they tried to close in on Mesa's seat of power. No injuries were immediately reported, but police made 22 arrests, among them protesters accused of brandishing dynamite, according to state television Canal Siete.
The protest marked the fourth week of unrest in which protesters have also thrown up road blockades, strangling the capital and causing gas and food shortages in this impoverished Andean nation of 9 million people.