Trump said in a Twitter post on Thursday.
"We do not aspire to be 'a nation that dwells alone, ' but that is how we were forced to stand at the beginning of the Yom Kippur War", he said, noting that American assistance arrived only toward the end of the war.
The SDF have been the main allies of US forces on the ground in the battle against Islamic State since 2014.
The SDF have been holding prisoner some 10,000 captured Islamic State group fighters.
The US military has taken custody of two high-profile Daesh militants previously held in Syria by the SDF and moved them out of the country to a secure location, a US official said. Explosions had rocked Tel Abyad earlier in the night, they said. Kurds said they were resisting the assault.
"Both Turkish and Kurdish forces have a track record of carrying out indiscriminate attacks in Syria that have killed scores of civilians", said Lynn Maalouf, Middle East research director for the group.
Turkish airstrikes were reported at the border towns of Tal Abyad, Ras al-Ayn and Qamilshli, as well as Ain Issa further south.
Turkish armed forces earlier said they had struck 181 targets with air strikes and howitzers since the start of the operation.
The operation dubbed "Peace Spring" by the Turkish government, began on Wednesday at around 4 p.m. with air raids and shelling while a ground offensive, involving Turkish soldiers and allied Syrian rebels, began at 11.30 p.m., reports Efe news.
Trump added that Turkey had committed to 'ensuring no humanitarian crisis takes place - and we will hold them to this commitment'.
"It's the actions of the Turkish government that concern Australia very seriously", he said.
Russia, Syrian President Bashar al-Assad's strongest foreign ally, urged dialogue between Damascus and Syria's Kurds on solving issues in northeast Syria.
Senior Republican senator Lindsey Graham argued the USA administration had "shamelessly abandoned" the Kurds.
Trump called the Turkish assault a "bad idea" and said he did not endorse it.
Republican Senator Lindsey Graham, usually a vocal Trump ally, has criticized his decision to withdraw USA troops from northeastern Syria and unveiled a framework for sanctions on Turkey with Democratic Senator Chris Van Hollen.
Democratic Senator Chris Van Hollen worked together with Republican Graham in preparing the framework of the legislation.
Investors are concerned about proposed USA sanctions on Turkey following the start of the incursion, including targeting Ankara's military transactions and US assets of President Tayyip Erdogan.
Aid workers said they had been told to leave by their organisations, and most had done so reluctantly. "That's what we're looking at right now, we haven't seen significant examples of that so far".
Germany's Foreign Minister Heiko Maas, warned that it will destabilise the region and risk a resurgence of the Islamic State.
Concerning the United States debt to Kurdish fighters he said "They didn't help us in the second world war, they didn't help us with Normandy ... but they're there to help us with their land".
Following the United States withdrawal from the region, Turkey has launched airstrikes and fire artillery at Kurdish armed forces positioned around the border of Ras al Ain, in the Kurdish regions of northern Syria on Wednesday.
Turkey says it intends to create a "safe zone" that would push Kurdish militia away from its border and eventually allow the repatriation of up to 2 million Syrian refugees.