Rodriguez was sworn in on Thursday by head of Congress Hormando Vaca Diez, who himself declined to assume the country's presidency.
In his inauguration speech, shortly after midnight, Rodriguez made his commitment to a new vote: "One of my functions will be to convene the electoral process to renew the representatives of the people."
He did not set a date for the polls, but the constitution stipulates that under such circumstances, new elections must be held within the next six months.
Mesa, who resigned on Monday, had more than two years left of his term in office, which he took over after his predecessor Gonzalo Sanchez de Lozada resigned, also under popular pressure, in 2003.
Congress met in Sucre, instead of its headquarters in La Paz, to avoid violent street protests by tens of thousands of farmers and workers demanding new elections and the nationalisation of the oil and gas industry.
The demonstrations, however, followed the lawmakers to Sucre where earlier they turned violent, with a protesting miner shot dead by soldiers on Thursday.