Donald Trump has called Turkish President Recep Tayyip Erdogan to congratulate him on his narrow victory in a much-disputed referendum granting sweeping new powers.

The US president also thanked Erdogan for supporting the US missile strike on a Syrian government airbase earlier this month.

A brief readout of Monday's (17 April) phone call, released by the White House, did not say whether Trump had raised concerns expressed by international observers monitoring Sunday's referendum over voting irregularities.

The slim victory of 51.4% was ruled valid by Turkey's electoral body.

But the Organisation for Security and Co-operation in Europe (OSCE) and the Council of Europe said the vote took place on an "unlevel playing field" and that "fundamental freedoms essential to a genuinely democratic process were curtailed".

Late changes in counting procedures "removed an important safeguard and were contested by the opposition", the report added.

"In general, the referendum did not live up to Council of Europe standards," said Cezar Florin Preda, head of the Council of Europe delegation.

Erdogan's victory, which approved a series of constitutional amendments, also led to concerns over the future of democracy in Turkey. The powers granted could potentially keep the Turkish president in office until 2029, scrap the job of prime minister and allow the president to directly appoint top public officials.

Trump's congratulatory message strikes a different tone to the statement issued by the US State Department, which urged Erdogan to "protect the fundamental rights and freedoms of all its citizens".

It also contrasts with more cautious responses from several European leaders, with some even saying the vote effectively ended Turkey's decade-long attempt to join the EU.

"With what happened yesterday, (Turkey's) membership prospects are buried, in practical terms," the Austrian chancellor, Christian Kern, said in a statement. "We are entering a new era."

German Chancellor Angela Merkel also warned that the "tight referendum result shows how deeply divided Turkish society is and that means a big responsibility for the Turkish leadership and for President Erdogan personally".

Erdogan and his supporters argue the changes brought by the referendum are necessary to ensure security as it continues to battle the Kurdish fighters.

They also come just eight months after the Turkish president survived a failed coup.