In a nationally televised address late Tuesday, Mesa said, "The only solution (for ending the protests) is an immediate election."
By law, Bolivia's leader of the Congress, Hormando Vaca Diez, is next in line for the presidency, as Mesa did not have a vice president. However the president urged Diez not to accept the position and asked the country's Supreme Court order immediate elections.
Congress is scheduled to meet Thursday to decide whether it will accept Mesa's resignation. The president resigned in March but Congress rejected the offer.
For several weeks, protests have gripped South America's poorest county and ground its capital, La Paz, to standstill causing food and fuel shortages.
Demonstrators want Bolivia to nationalize its oil and gas industry.
Last month Mesa raised taxes on earnings by foreign petroleum companies operating in Bolivia to 50 percent.
However the move proved too little for the thousands of miners, laborers and indigenous people who have taken to the streets demanding total nationalization and a rewrite for the constitution.