The meeting between Trump and Erdogan comes during an uproar in Washington over reports that the US president disclosed sensitive information regarding Islamic State to senior Russian officials during a White House meeting last week.
Despite the global criticism of the way the referendum was conducted, Trump called Erdogan afterward to congratulate him on the victory.
Turkey, the only majority Muslim country in the North Atlantic Treaty Organisation alliance, hosts more than 2,500 USA troops at Incirlik, a key launching point for air strikes against the Islamic State.
Ankara regularly clashed with Obama's White House over the extradition of opposition leader Fethullah Gulen, who has lived in self-imposed exile in rural Pennsylvania since 1999.
According to the White House, Trump and Erdogan are expected to "discuss how to further strengthen our bilateral relationship and deepen our cooperation to confront terrorism in all its forms".
President Trump can sympathize. "We know the new United States administration will not let these hopes be in vain", Erdogan said. If we are strategic allies, we have to make decisions as an alliance.
Erdogan believes Gulen was behind a failed military coup in July last year, but the USA has said there is not enough evidence to send the 76-year-old Muslim cleric back to Turkey.
"We support Turkey in the first fight against terror and terror groups like ISIS and the PKK, and ensure they have no safe quarter", Trump said.
Turkey could disrupt the Pentagon's battle against the jihadists in several ways.
Washington has sought to placate Turkey by saying that the weapons will be metered out carefully, and insisting it still wants to "work with the Turks.to take Raqa down". Erdogan accused the Trump administration on Wednesday of siding with terrorists. So why is the USA making this change?
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Giuliani and Mukasey's potential for conflicts-of-interests in the Zarrab case have faced the scrutiny of a federal judge in NY since February.
In this photo taken Sunday, May 14, 2017, Turkey's President Recep Tayyip Erdogan speaks during the Belt and Road Forum at the China National Convention Center in Beijing, China. They cited the weakening of democratic institutions, stifling of fundamental human rights, mass arrests and civil society restrictions that have been taking place even before a constitutional referendum in April gave Erdogan increased powers and extended his time in office. Both Turkey and the United States have officially designated it a terrorist group. "It's because Zarrab has all sorts of dirty laundry on Erdogan".
Omar Abo Laila of the activist-run Deir Ezzor 24 says 15 homes in the town were destroyed in the raid on Monday. If Zarrab enters into a plea deal, his cooperation with the US government could lay such connections bare. "He can start putting American principles and priorities first by rejecting Ankara's gag-rule against honest US remembrance of the Armenian Genocide".
Turkish officials have repeatedly asked the United States to extradite Gulen, who oversees a vast educational and religious network in Turkey, over his suspected involvement in that episode.
Erdogan again raised his country's vehement opposition.
Among other allies in Trump's orbit who have pushed for a softer line on Turkey is his former national-security adviser Michael Flynn.
The Trump team was once reportedly considering kidnapping Gulen and sending him back, but it is not clear what their policy is now.
"We are determined to expand our relations and I believe my current official visit to the United States will mark a historical turn of tide", the Turkish leader added.
But during their appearance on Tuesday, Trump made no mention of Erdogan's record on dissent and free speech, although they have been areas of concern for some Western leaders.
The US-backed Syrian Democratic Forces militia is set to lead the fight for the Islamic State group's bastion of Raqa, but its role has stoked tensions between Washington and Turkey.