Trump tweeted on Thursday that the US has three options regarding the situation in Syria: "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," Xinhua news agency reported.
"I hope we can mediate," Trump told the press later when he was asked about the three options.
Trump also cautioned Turkey against actions beyond limits.
"Turkey knows where I stand... We are going to possibly do something very, very tough with respect to sanctions and other financial things," the President added without elaborating.
A senior State Department official reaffirmed Trump's warning to Turkey in a teleconference briefing later in the day, saying that the US was willing to impose significant costs if "Turkey acts in a way that is disproportionate, inhumane, or otherwise goes beyond the lines that the President has in his own mind".
The official also revealed that Turkey had, at various levels and for multiple times, asked for US military support for its military operation, which Washington had rejected.
Republican Senator Lindsey Graham and Democratic Senator Chris Van Hollen on Wednesday announced a framework for sanctions against Turkey for its ongoing military campaign in northeast Syria.
The framework includes sanctions on senior Turkish government officials and prohibition of all US military business and transactions with Turkey, among others.
Turkish Foreign Minister Mevlut Cavusoglu responded on Thursday that Ankara would retaliate if the US imposed sanctions over its offensive into northeast Syria, according to media reports.
Turkey regards the Kurdish-led Syrian Democratic Forces (SDF) as an extension of its Kurdistan Workers' Party, which is listed as a terrorist organization by Ankara, while the US considers the SDF an ally in the fight against the Islamic State terror group.
Earlier Wednesday, Turkey launched military operations targeting the Kurdish forces in several parts of northeast Syria after the US started pulling its troops out of there following a recent decision.
Syrian Foreign Ministry condemned the Turkish military offensive on Kurdish positions in northern and northeastern Syria, stressing the Syrian government's determination to confront the "Turkish aggression by all means".
( With inputs from IANS )