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He said he would discuss the issue at a meeting with U.S. President Donald Trump next month.
The U.S. has provided air cover and other support to Kurdish forces battling ISIS. NATO member Turkey views the Syrian Kurdish forces as an extension of its own Kurdish insurgency, and launched airstrikes against them last week.
U.S. troops have since been seen patrolling the tense border.
Erdogan said: "We will be forced to continue (our offensives). We won't provide a date and time for when we'll come. But they will know that the Turkish military can come."
President Tayyip Erdogan declared victory in a referendum on April 16 to grant him sweeping powers in the biggest overhaul of modern Turkish politics.