Socialist Prime Minister Victor Ponta's efforts to unseat the conservative Basescu have brought criticism from the European Union, which accused him of undermining the rule of law and intimidating judges.
The row over Basescu has delayed policymaking, sent the leu currency plunging to record lows, and pushed up borrowing costs. It also raised concern about the future of Romania's €5 billion ($6.2 billion) International Monetary Fund-led aid deal.
The election bureau said the voter turnout was 46%, below the 50% threshold Ponta's leftist Social Liberal Union (USL) needed to make the referendum valid.
Exit polls showed more than 80% of those who went to the ballot box had voted to remove the president.
"The flame of democracy has remained alight. Romanians have rejected the coup d'etat," Basescu said.
Ponta says government will respect outcome
Ponta, whose government took office in May, suspended Basescu and held the referendum to seek popular backing for the impeachment for overstepping his powers. The president is unpopular for backing austerity and for perceptions of cronyism.
The electoral bureau's figures have a margin of error of three percentage points and do not include Romanians voting abroad, but it is now almost certain that final figures – likely to appear today (30 July) - will show turnout was under 50%.
Opinion polls had shown some 65% of Romanians wanted to remove the former sea captain from office, but the opposition had called for a boycott of the vote and many people were on holiday.
The president's most important power is nominating the prime minister, which could be crucial after a November election that may leave a split parliament. The president also appoints the chief prosecutor and some judges, including to the Constitutional Court.
That court, which previously said the threshold had to be observed, will make the decision on the vote's validity this week.
"The Romanian government will respect all decisions of the Constitutional Court and will act as a factor of stability in the next period, regardless of whether the referendum is validated or not," Ponta said.
Ponta wanted minimum turnout rule scrapped
Romania has made progress since the 1989 overthrow of communist dictator Nicolae Ceausescu and joined the EU in 2007, but the economy slipped back into recession in the first quarter of this year and pockets of severe poverty remain.
Ponta felt the full weight of EU wrath after his government took on the Constitutional Court, threatening to replace judges and reduce its powers, and ignoring one of its decisions. Brussels said it was concerned about the government's respect for the rule of law, democratic procedures and the judiciary.
The government had tried to make it easier to impeach Basescu by removing the minimum turnout rule, but was forced to back down following harsh EU criticism and a Constitutional Court ruling that a 50 percent turnout was obligatory.
Basescu initially urged Romanians to vote against what he called a coup d'etat, but this week he changed his mind and he and his allies, the opposition Democrat Liberal Party (PDL), asked supporters to boycott the referendum, citing concern about the possibility of electoral fraud.