"The United States continues to support Turkey's democratic development, to which commitment to the rule of law and a diverse and free media remain essential". Some voters had been unable to cast their ballots in private, he also said.
Erdogan also lashed out at an OSCE report critical of Turkey's handling of Sunday's referendum.
"The rule of a match can not be changed while the match is being played, this is a universal rule", he said.
Sunday's referendum endorsed by a narrow margin the largest overhaul of Turkey's political system since the founding of the republic almost a century ago, giving Erdogan sweeping authority over the North Atlantic Treaty Organisation member-state.
The referendum was presented by the government as a vote for better governance and stability in Turkey, after a long history of frequent government rotations, clashes between prime-ministers and presidents and military coups.
Turkey's top electoral board will consider objections Wednesday to the way the country's referendum was run, according to Turkey's semi-official Anadolu news agency.
He also said the electoral board's last-minute decision to allow unstamped ballots had prevented proper record-keeping, meaning that it was now impossible to determine how many invalid or fake votes may have been counted.
Speaking to reporters aboard Air Force One, White House spokeswoman Sarah Huckabee Sanders said Trump's call to Erdogan on Monday was focused primarily on the "shared interests as a North Atlantic Treaty Organisation ally and a partner there".
Kirkland's Chappell edges Koepka by 1 stroke to win Texas Open
He sank a 56-foot putt to birdie earlier at No. 6, so he 2-putted for the birdie at 17 and ran in another birdie at 18. Meanwhile, Kevin Chappell survived a roller-coaster front nine with three birdies, one double bogey and three bogeys.
Opposition parties filed formal requests Tuesday to void the results over voting irregularities, particularly an electoral board decision to accept ballots without official stamps, as required by Turkish law.
Turkey's electoral authority rejected appeals to annul the referendum granting President Tayyip Erdogan wide new powers, but the main opposition CHP party said it will maintain its legal challenge to a vote it has said was deeply flawed.
He went on to warn that calling for street protests is unacceptable. "It is wrong to speak after the people have spoken". "The opposition should not call people to take to the streets and say they do not recognize election results".
Reminded that "it was a win with slimmest of margin 51.4 percent to 48.6" in the referendum, Erdogan said a win was a win.
He said there were 3 million refugees in Turkey and the European Union had pledged a 6 billion euro aid package to help Turkey care for the millions of refugees, but had so far received only 725 million euros ($777 million) from UNESCO and $550 million from the UN High Commissioner for Refugees.
Turkish Foreign Minister Mevlut Cavusoglu said Wednesday that the two leaders would sit down together before a North Atlantic Treaty Organisation summit scheduled for May 29-30 in Brussels.
"The German government takes the report by the OSCE and the Council of Europe very seriously, and we expect Turkey to do so", German foreign ministry spokesman Martin Schäfer told reporters in Berlin.