The Turkish government rejected the criticism as "black propaganda" and vowed to push ahead with the military operation.
More than 100,000 people have been displaced as a result of the Turkish offensive – 65,000 of them from the Turkish-Syrian border town Ras al-Ayn – according to the UN World Food Program.
"More people are leaving on a daily base and those numbers will go up," the UN agency said.
In a statement late Friday, Turkey's Defense Ministry said it did not open fire on the US facility and said it struck a Kurdish position after a Turkish one had been attacked with machine guns and mortar fire 1 kilometer (1,100 yards) from a US observation post.
The statement added that Turkey ceased firing after being contacted by US officials.
US officials said US troops left the post after it came under fire. It is the first time a coalition base was in the line of fire since Turkey's offensive began.
"The US demands that Turkey avoid actions that could result in immediate defensive action," DeWalt said.
Conflicting claims on town capture
On Saturday, the Turkish military claimed that it had taken control of Ras al-Ayn.
The Turkish Defense Ministry tweeted in English that "the town of Rasulayn, located east of the Euphrates, has been brought under control."
The Kurdish-led Syrian Democratic Forces have denied Turkey's claim, saying some of their fighters had made a "tactical retreat" from one neighborhood. The Britain-based Syrian Observatory for Human Rights, an opposition war monitor, confirmed that Turkish troops had entered the town, but said that fighting was still ongoing.
The United Nations on Friday said 100,000 people had been displaced by Turkey's operation, with the World Food Programme (WFP) warning of a impending humanitarian crisis in Syria's border region.
The Observatory said 10 civilians were killed on Saturday in a Turkish air strike in the region, taking the civilian death toll from the offensive to 28.
US could 'shut down' Turkish economy
Earlier Friday, the US warned that Ankara could face "powerful sanctions" if its operations targeted civilians.
Speaking at the White House, US Treasury Secretary Steven Mnuchin said that the US could "shut down the Turkish economy" if Ankara goes too far.
Mnuchin emphasized that although sanctions had not yet been activated, the US Treasury would be putting financial institutions on notice that measures "targeting any person associated with the government of Turkey, any portion of the government," could be possible.