Turkey and the United States are due to start joint military patrols in the area on Sunday, as part of an agreement for what Turkey says will become a "safe zone" along the border inside Syria.
Turkey, which hosts 3.6 million refugees from the Syrian conflict and already holds territory in northwest Syria, wants to extend its military presence into the northeast to push back Syrian Kurdish militia fighters from the border and establish conditions for the return of a large number of Syrians.
Describing his plan to meet Trump at the U.N. General Assembly, Erdogan said they would discuss "what kind of steps we will take" along the Syrian border east of the Euphrates river.
"There are differences between what is said and what has been done," he said in a speech in the Turkish city of Eskisehir. "We must resolve this."
He said Turkey could not accept military training by U.S. forces of Kurdish Syrian YPG fighters, who have been Washington's main ally on the ground against Islamic State in Syria but are designated a terrorist organization by Turkey.
Erdogan also reiterated a plan he first spelt out on Thursday to move a million refugees to northern Syria, a project he said would require international support to build new homes.
"We can undertake the construction. You give us financial support," he said. "They say good. Then come on, show your support. But nothing."
Turkey has frequently complained about what it says is a lack of international support to help it host the refugees, some of whom have been in Turkey since the start of Syria's conflict eight years ago.
Erdogan says Turkey has spent $40 billion supporting the refugees. The European Union, which signed an accord with Turkey three years ago offering aid in return for Turkish steps to stem the flow of migrants to Europe, says it has disbursed more than 5 billion euros of support.Turkey's Chief of General Staff General Yasar Guler told his U.S. counterpart General Joseph Dunford that the two countries should waste no time setting up the "safe zone," Turkey's Defence Ministry said on Saturday.