Investors have been closely watching tense ties between Ankara and Washington in recent months, with the NATO allies at odds over a range of issues, including policy differences in Syria and Turkey's purchase of Russian missile defence systems.
The lira declined more than 1.6%, trading at 5.795 at 1600 GMT, after closing at 5.7000 on Friday. Earlier, it slipped as far as 5.8195, its weakest level since September 3.
Turkey's dollar bonds also fell, with the 2038 issue down 1.3 cents.
Turkey's lira lost nearly 30% against the dollar last year, over concerns about political interference with monetary policy, as well as a deterioration in ties between Washington and Ankara. It is down about 8% this year.
Turkey's BIST100 main share index was down 0.45%, while the banking index declined 1.72%.
Turkey has repeatedly threatened to carry out an incursion against the US-backed Kurdish YPG militia in northeast Syria, accusing the United States of stalling efforts to establish a "safe zone" there along the Turkish border.
Following a phone call between Trump and Turkish President Tayyip Erdogan, the White House said on Sunday US forces would not support Turkey's incursion and would leave the area.
On Monday, Trump threatened to "totally destroy and obliterate" the Turkish economy if Turkey took any action he considered "off-limits".
"While the statement from the United States gives a green light to the military operation in Syria that Turkey has mentioned for a long time, it leaves many question marks regarding how the process will develop," said a forex trader, who did not want to be named.