GRAND RAPIDS, Mich. — Facing a torrent of criticism over his comments seeming to condone the hacking of Hillary Clinton’s emails by Russian intelligence services, Donald J. Trump and his allies on Thursday sought to tamp down his remarks, with Mr. Trump saying he was simply being “sarcastic.”

In public interviews and private conversations on Thursday, Mr. Trump; his running mate, Gov. Mike Pence of Indiana; and campaign staff members contended that Mr. Trump was being facetious when, during a news conference on Wednesday, he said he hoped Russia would be able to find Mrs. Clinton’s missing emails.

“Of course I’m being sarcastic,” Mr. Trump told “Fox and Friends” Thursday morning as his aides accused the news media of misconstruing his remarks.

And in an interview Thursday with the conservative radio host Laura Ingraham, Mr. Pence repeatedly said that Mr. Trump was merely joking.