Mularkey made the decision so he could focus instead on the Falcons' playoff game next week, a team source told ESPN NFL Insider Adam Schefter, who first reported the development.
John Elway, the Broncos' new executive vice president of football operations, who is spearheading the search, said via his official Twitter account: "I respect the decision that Mike Mularkey has made to not interview with the Broncos at this time."
Mularkey still will go through with his previously scheduled interview Saturday with the Cleveland Browns. He is doing so because they called first and he feels a certain sense of obligation, a team source told Schefter.
Mularkey still wants to be a head coach, and would interview with Denver later if it still had its opening after the Falcons' season ended, according to the source. But for now, he wants to keep as much of his focus as possible on the Falcons' upcoming playoff game and doesn't want to have to prepare for coaching interviews on back-to-back days.
Mularkey was a head coach for two seasons at Buffalo and served as an offensive assistant with the Dolphins, Steelers and Buccaneers.
The Falcons (13-3), as the No. 1 seed in the NFC, have home-field advantage throughout the conference playoffs and have a bye this week. They'll face the lowest-remaining NFC seed Jan. 15.
With Mularkey scrubbing his interview, the Broncos' search committee that includes general manager Brian Xanders, team president Joe Ellis and owner Pat Bowlen, will remain in Denver preparing to interview New York Giants defensive coordinator Perry Fewell and interim Denver coach Eric Studesville, both on Sunday.
A team spokesman said Thursday there was nothing scheduled with Stanford coach Jim Harbaugh, whom Elway was hoping to line up for an interview.
Elway said he wanted to hire a coach who already had head coaching experience, preferably in the NFL, and both Fewell, 48, and Studesville, 43, have been interim head coaches, Fewell for seven games in Buffalo in 2009.
"I don't believe anybody that's not had that NFL experience can make that jump -- other than Harbaugh. There's nobody [else] in the college ranks that we're interested in talking to," Elway said. "And preferably we'd like to have some head coaching background in the NFL, but it's not a must. If there's a guy who's a coordinator that's up and coming and shows that he can be the head coach and understands that, then he'll be the guy."
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.