At least five civilians and three Kurdish fighters were reportedly killed.
On Saturday, Turkish President Recep Tayyip Erdogan announced that the country had "completed our preparations and action plan" and was ready to launch a "ground and air operation" east of the Euphrates river, with the goal of establishing "peace" by clearing the region of "terrorists".
The abrupt policy shift has been widely criticized in Washington, including by members of his own party.
"Turkey has committed to protecting civilians, protecting religious minorities, including Christians, and ensuring no humanitarian crisis takes place-and we will hold them to this commitment", Trump said. In his statement, Trump emphasized that there are no American soldiers in the area under attack.
The United Nations Security Council will meet on Syria behind closed-doors on Thursday, diplomats said.
Marxist Leninist Communist Party - a far-left armed Turkish group that is illegal in Turkey, the MLKP have fought against IS alongside the YPG since 2012.
AFP journalists witnessed the arrival of a large convoy of vehicles in the Turkish town of Akcakale in Sanliurfa province overnight.
"All the shops around me are open, except that there are no people", Mohammed said in a telephone interview. "There's smoke, columns of smoke rising above the city", the 30-year-old, who is a part of Women Defend Rojava campaign, said by phone.
Foreign Minister Heiko Maas said in a statement that "we condemn the Turkish offensive in the northeast of Syria in the strongest possible terms".
Turkey has also spoken about creating a space inside Syria where two million Syrian refugees who are now hosted in Turkey could be settled.
In the build-up to the anticipated offensive, Syria had said it was determined to confront any Turkish aggression by all legitimate means.
For Turkey, which views Kurdish YPG fighters in northeast Syria as terrorists due to their ties to militants waging an insurgency inside Turkey, an influx of non-Kurdish Syrians would help it secure a buffer against its main security threat. "The main security threat against Turkey is the PKK". "We call on our Kurdish, Arab, Assyrian, and Syriac people to strengthen their unity and stand by the SDF in defense of their land", said the SDF. With Turkey turning away from that agreement, however, the USA troops at the center may be called on to instead monitor the Turkish operation and make sure that US troops stay out of harm's way, the US officials said.
U.S. Senator Lindsey Graham, a South Carolina Republican who is one of Trump's closest confidants in Congress and a frequent golf partner, has angrily split with Trump over Syria.
The Pentagon would not confirm to Military.com reports that the Syrian Democratic Forces, which drove the Islamic State from its last strongholds in Syria, is now turning to face the more imminent threat from Turkey.
The Kurdish-led authority in northern Syria declared a state of "general mobilization" before calling on its people to head toward the border "to fulfill their moral duty and show resistance in these sensitive, historic moments".
"Our mission is to prevent the creation of a terror corridor across our southern border, and to bring peace to the area", Erdogan said on Twitter.
Another senior administration official who spoke to reporters on Monday said Turkey "would bear full responsibility" if the Islamic State (IS) reconstitutes in the wake of the crisis, but did not make clear how the United States planned to hold Ankara responsible for maintaining overcrowded detention facilities now under Kurdish control, including Al-Hol.
Kurdish officials indicated on Tuesday afternoon that Turkish forces had begun shelling positions on the border, but no injuries had been reported.