Trump, who pulled U.S. troops out of the area before the Turkish attack, said on Twitter that the United States had three options.
"We have one of three choices: Send in thousands of troops and win Militarily, hit Turkey very hard Financially and with Sanctions, or mediate a deal between Turkey and the Kurds!" Trump said.
"I hope we can mediate," Trump said when asked about the options by reporters at the White House.
"Turkey knows where I stand," he said.
Trump said he did not think Americans wanted to see the U.S. military sent back into the region.
"We are going to possibly do something very very tough with respect to sanctions and other financial things," Trump said without elaborating.
Trump ordered the pullback after a phone call with Turkish President Tayyip Erdogan on Sunday, prompting rare criticism from senior figures in his own Republican Party who accuse him of deserting loyal U.S. allies - the Syrian Democratic Forces (SDF) led by Kurdish YPG militia.
The SDF have been the main allies of U.S. forces on the ground in the battle against Islamic State since 2014.
Trump has called the Turkish assault a "bad idea," said he did not endorse it, and threatened to devastate the NATO ally's economy if Ankara's incursion into Syria wipes out the Kurdish population there.