"We are really talking about a dead heat at the moment. So it would be better to hold your enthusiasm and calmly wait for results," Vice President Alvaro Garcia told reporters. "All your celebration may well turn into weeping."
He did not immediately say what percentage of the vote was counted. But he said media projections signaling a no vote had prevailed could well be wrong.
Earlier, local media projected that Bolivians had denied Morales' bid to seek a fourth term and potentially extend his presidency until 2025.
Already the country's longest serving leader, Morales lost the referendum vote 52.3 per cent to 47.7 per cent, according to unofficial figures cited on private ATB television. Unitel television gave the "no" vote as 51 per cent to 49 per cent.
If confirmed officially, it would be the worst - and first - national political defeat for Morales, who has led the Andean nation for a decade.
Voting yesterday was mandatory, and some 6.5 million Bolivians were eligible to cast ballots.
Last month, Morales became the longest serving president since Bolivia's independence from Spain in 1825 - a rare accomplishment in a country known for military coups and shaky, short-lived governments.
Now 56, Morales is also Bolivia's first democratically elected president of indigenous heritage.
Morales has overseen robust economic growth in Bolivia, but opponents accuse him of presiding over corruption and investing in flashy infrastructure projects at the expense of health and education.
Under the current constitution adopted in 2009, sitting presidents can only seek re-election once. But Bolivia's Supreme Court ruled that Morales's first term was exempt from the rule, allowing him to run again in 2014.
Last month, he became the longest serving president.
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