WASHINGTON—President Donald Trump is considering broad changes to his communications team and strategy, which he blames for failing to contain the controversy surrounding his firing of former FBI DirectorJames Comey, according to multiple administration officials.

Among other moves, Mr. Trump is again weighing replacing Press Secretary Sean Spicer, who returned to the briefing-room lectern on Friday after two days away on Naval reserve duty. But the president is considering a larger reorganization of his team, a White House official said. Since Wednesday, a senior communications staffer has been reaching out to supportive cable TV surrogates to gauge their interest in joining the staff.

Additionally, in a taped interview set to air Saturday, Mr. Trump said he is considering abolishing the century-old practice of daily press briefings in favor of conducting his own briefing every two weeks, according to a preview released by Fox News. In that interview, the president called Mr. Spicer a “wonderful human being” but declined to answer a question about whether he would remain in his post.

Mr. Spicer didn’t respond to a request for comment.

Part of the challenge in any media strategy is managing the president’s own tweets and other communications. On Friday, Mr. Trump fired off a round of tweets that underscored the degree of difficulty.