The post also drew criticism from a spokeswoman for the United Nations High Commissioner for Refugees, which is providing aid to Syrians.

“Syrian refugees are fellow human beings who have left their country to escape war and terrorism,” Melissa Fleming, the spokeswoman, said in an email on Tuesday. “Depictions like these are dehumanizing, demeaning and dangerous.”

Emails sent to the campaign of Donald J. Trump, the Republican presidential nominee, seeking comment were not immediately answered on Tuesday. But Mr. Trump’s running mate, Gov. Mike Pence of Indiana, criticized the blowback in an interview on MSNBC.

“It is remarkable to me to see the level of outrage about a metaphor used by Don Jr.,” he said, adding, “All the while our F.B.I. and public-safety officials tell us that we can’t know for sure who those people are coming into this country.”

The war in Syria has killed over 400,000 people and has uprooted nearly five million. Last month, the United States said it had met its goal for the year, welcoming its 10,000th Syrian refugee. State Department statistics say that fewer than 20 of the 785,000 refugees settled in the United States since the Sept. 11 attacks have been arrested on terrorism charges.

On the campaign trail, Mr. Trump has likened the influx of Syrian refugees to infiltrators in a Trojan horse and said he would like to “build a safe zone in Syria, build a big, beautiful safe zone, and you have whatever it is, so they can live.”