Ms. Brzezinski said in February that she would no longer book Ms. Conway on the show, because she and Mr. Scarborough had come to believe that the White House counselor was prone to spreading falsehoods. On the air last week, she renewed that criticism, calling Ms. Conway “not credible” and chiding CNN for featuring Ms. Conway.

“Your hosts look pained when they interview her because they know they’re just doing politics porn,” Ms. Brzezinski said, addressing the rival network.

Ms. Conway has been a frequent target of media critics since she justified the White House’s reports about the size of Mr. Trump’s inauguration crowd by calling them “alternative facts” in January. A clip of Anderson Cooper, the CNN anchor, rolling his eyes at her during an interview drew attention last week, and Ms. Conway later called the reaction “possibly sexist,” and saying that it was typical of an anti-Trump bias in the media.

The hosts of “Morning Joe,” fixtures of the same Washington punditry scene that Ms. Conway has frequented since the 1990s, have in the past enjoyed a congenial relationship with Mr. Trump, who reportedly offered to officiate their wedding. But they have criticized him more harshly in recent months, and Mr. Trump has said in interviews that he has stopped watching the network.