President Evo Morales asked Bolivians to wait "calmly" for the official result of Sunday's referendum, saying the outcome could still go either way.
"I am asking all the social movements, of both 'yes' and 'no,' to calmly and responsibly await the final result from the electoral commission," he said in a national broadcast on Monday.
Morales, who was first elected in 2006, is now on his third term and is trying to change the constitution to remain in power until 2025.
The result of the referundum will define whether Morales, Bolivia's first indigenous president, should be allowed to run for the elections in 2019.
By Monday midnight 80 percent of the votes has been counted. The "no" vote was ahead with 55 percent, while only 45 percent of voters chose "yes," according to Bolivia's electoral commission.
However, the exit polls indicated a much closer result.
Supporters of Morales say he has brought stability and increased social spending in Bolivia, one of the poorest countries in the region.
Morales, who was once a coca grower, said if he failed in the referendum he would retire to his farm after his term is up but that he would not give up the "struggle."
"Life goes on. If the 'no' wins the struggle will continue, the administration will continue, I have a lot of responsibilities and it's no good despairing whatever the result," he said.
The proportion of "yes" votes is expected to increase as ballots are counted from rural areas and outside the country.
As such, celebrations in the "no" camp has not yet started.