Trump also offered compassion and support for "horrible terrorist attacks" against the Turkish people in recent years.
But Trump was one of the first leaders to get on the phone and congratulate Erdogan for his victory, so it is unclear whether he will express any concerns over the development.
Turkey has leverage of its own, not least being the importance of its Incirlik air base, which hosts about 1,500 US troops and is used for air strikes against the Islamic State by the USA and its allies.
President Donald Trump will meet with Turkish President Recep Tayyip Erdogan in Washington, D.C., for the first time on Tuesday, one week after the White House announced plans to arm Syrian Kurds fighting the Islamic State despite fierce opposition from Ankara.
The Turkish leader said that Turkey had "notified our friends" about Gulen's alleged involvement in the coup.
Flynn was forced out as National Security Agency director after less than a month on the job, after President Trump said he lied to Vice President Mike Pence about his contacts with the Russian ambassador to the U.S. Flynn also had worked for Russian companies, including some closely linked to the Russian government.
It is believed that the two will discuss several matters including Trump's decision to arm the Syrian Kurds.
A recent USA decision to provide heavier arms to the Kurds has angered Turkey, a North Atlantic Treaty Organisation ally.
The Trump administration has ramped up efforts to respond to the crisis in Syria, taking unprecedented action against Syrian President Bashar Assad's government over its use of chemical weapons against civilians.
Turkish officials have spoken enthusiastically about Trump's election as a chance to turn a new page, but hopes could have been dashed last week when the Pentagon confirmed that it has increased its support for the YPG by directly arming its fighters ahead of the battle to oust the Islamic State from its de facto capital in Syria.
The Turks see the Kurdish fighters as terrorists and are fiercely opposed to the USA plans.
"The best thing to be hoped for from this is that they come out saying that they are both determined to work on the relationship and that Turkish concerns are being taken into account", said Aliriza, who described the move to arm the YPG as an natural disaster in U.S.
But the SDF's ranks, which estimates place at anywhere between 25,000 and 45,000 fighters, remain dominated by the YPG, which also retains control of the alliance's command, analysts say. They think "Turks are going to have to swallow it" and after protesting for a while, Ankara will not do much to hinder that decision because it will need the U.S.in the long-term and have no other options. Weeks later, Mr Trump is still beaming about the meeting and how great Mr Xi is. Observers, meanwhile, will be closely watching how Trump handles Turkey's deteriorating human rights situation. Erdogan recently won a referendum in Turkey that gave him even more power.
Expanding his probe again on Monday, Berman signed a two-page order demanding that Giuliani and Mukasey produce any "work performed for President Trump's administration, including participation on United States commissions, such as those relating to the so-called "Muslim ban" executive order".
"Military equipment was ordered by Turkey and the president [Erdogan]", Trump stated.
Foreign allies may see things differently.
Mr. Trump was asked by reporters following the statement about his alleged disclosure of classified information during his meeting last week with Russian Foreign Minister Sergey Lavrov, a meeting he on Tuesday called "very, very successful".
National Security Advisor HR McMaster said that "at no time were any intelligence sources or methods discussed and no military operations were disclosed that were not already known publicly".