“Whether you call them refugees or illegals, there’s no difference — we want them out,” added Mr. Kasidiaris, whose party last week also threatened a group of migrants camped at the port of the Greek island of Chios.

He added that Golden Dawn aligned itself with statements made by Donald J. Trump, who had called for Muslims to be barred from the United States. “It would be a very positive development if he were to be elected president,” Mr. Kasidiaris said.

The clashes in Idomeni unfolded when a group of migrants acting as emissaries for those in the Idomeni camp approached the barbed-wire-topped border fence and asked the Macedonian police to open it to let them continue north. When the request was declined, the men apparently threw rocks at the police, who responded by firing tear gas at the growing crowd.

Doctors Without Borders and several other humanitarian groups in Idomeni said in statements that they were treating numerous people for injuries, including men who had been knocked unconscious as well as children, after tear gas blew into hundreds of flimsy pup tents where the migrants have been living in the mud over the last several weeks.