With 51.4 percent of the vote, President Recep Tayyip Erdoğan's "yes" campaign won Turkey's landmark referendum for a new political system, giving enormous centralized power to the president.
A statement issued by the President's Special Adviser on Media and Publicity, Mr Femi Adesina, in Abuja on Tuesday said Buhari particularly congratulated Turkish President, Recep Tayyip Erdogan for his foresight.
Monitors from the Organization for Security and Cooperation in Europe, who also listed numerous irregularities, said the board's move undermined important election safeguards.
The spokesperson for the European Commission, Margaritis Schinas, said the call comes after Turkey rejected worldwide observers' criticism of the referendum on Sunday, in which over 51 per cent of voters supported granting greater powers to President Recep Erdogan.
He declined comment on a possible change in the result of the referendum after any recount, but said the election commission's decision to allow incorrectly or non-stamped envelopes was a definite violation of Turkish law.
The French government said it would "follow with great care" the global monitors' final report in coming weeks, particularly in relation to a reported last-minute change of rules by the electoral boards to allow ballots that had not been officially stamped.
Mehmet Hadimi Yakupoglu, the Republican People's Party's representative to the High Electoral Board, said the party had asked the board to annul Sunday's referendum "because we weren't able to ensure election safety".
Turkey's prime minister says opposition parties have the right to file objections to the outcome of a recent referendum on expanding presidential powers, but warned that calling for street protests was unacceptable. "Everyone should respect the outcome, especially the main opposition". We are invited by the Turkish authorities to observe. He accused the board of "changing the rules midgame".
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Turkey's prime minister has called on the opposition to respect the result of a referendum that will expand the powers of the office of the president.
The changes allow the president to appoint ministers, senior government officials and half the members of Turkey's highest judicial body, as well as to issue decrees and declare states of emergency.
"I suspect the result was narrower than what Erdogan expected", said Howard Eissenstat, associate professor of Middle East History at St. Lawrence University in Canton, New York.
The new presidential system takes effect at the next election, now slated for 2019.
Under the outgoing constitution, the president had been required to remain impartial and renounce party political ties.
Meanwhile, OSCE monitors were seen entering the Supreme Electoral Board headquarters.
According to the spokesperson for the European Commission, Margaritis Schinas, the call came after Turkey rejected worldwide observers' criticism of the referendum on Sunday.
Ms. Schinas said: "We call on all actors to show restraint and on the authorities to launch transparent investigations into these alleged irregularities found by the observers".