The more James Comey showed up on television discussing the FBI’s investigation into possible ties between the Trump campaign and Russia, the more the White House bristled, according to aides to President Donald Trump.

Frustration was growing among top associates of the president that Mr. Comey, in a series of appearances before a Senate panel, wouldn’t publicly tamp down questions about possible collusion with Russian interference in the 2016 presidential race. A person with knowledge of recent conversations said they wanted Mr. Comey to “say those three little words: ‘There’s no ties.’”

In the months before his decision to dismiss Mr. Comey as head of the Federal Bureau of Investigation, Mr. Trump grew unhappy that the media spotlight kept shining on the director. He viewed Mr. Comey as eager to step in front of TV cameras and questioned whether his expanding media profile was warping his view of the Russia investigation, the officials said.

One White House aide, speaking after Mr. Comey’s dismissal, described him as a show horse.