Nagle said she hoped the developments send a strong signal to Syracuse voters that something is amiss.
"This is a truly tragic loss for our city," she said of the resignations.
While declining a request for an interview, council member Karianne Lisonbee offered her reaction in a short email, saying she wished Carlson and Rice "the very best in their new endeavors."
"They are both capable, strong men," she wrote. But Lisonbee called the claim that people with backgrounds in the military and the legal profession would resign "over 'discord' is, on its face, suspect."
The mayor described Rice as a top-notch manager who had been instrumental in guiding Syracuse out of financial crisis in a little more than two years as the city's top administrator. She and other colleagues credited him with improving employee morale, rebuilding budget reserves, consolidating the city's utility, legal and engineering costs and restoring much-neglected spending on road maintenance.
"Every single idea he's had has turned out to be the best idea," two-term councilman Douglas Peterson said.
Rice, a 53-year-old retired U.S. Marine colonel, will leave July 23 to take a high-profile civilian position as director of operations for the Marine Corps Installations Command at the Pentagon in Washington, D.C. a post he said gave him "a great chance to get back to the Marine Corps."
Rice offered high praise for city staff and said he felt "proud of the team we've built," but he added that the political climate at City Hall was a contributing factor in his leaving.
"I would never leave a fight. I'm pretty ornery," Rice said. But frequent clashes with city council members especially when their ire has been directed at people he supervised "haven't made it as pleasant as I would like."
Carlson, 33, hired on as Syracuse's first full-time city attorney in December 2011, ending many years of Syracuse out-sourcing both its criminal and civil legal services. "It might take just take two people to replace him," Peterson said.
Nagle called Carlson "a one-stop shop" for legal expertise and "a quick study" on often-complex issues the city faced.
Carlson now will step down at the end of June to join Salt Lake County District Attorney Sim Gill's office as a criminal prosecutor. "I've enjoyed my time in Syracuse," he said, "but I'm looking forward to moving on."
He said that as the legal adviser to both Nagle and council members, he often was caught in the middle of their increasingly bitter disagreements. "When there is conflict," Carlson said, "there is no real way for me to win."
Syracuse has seen explosive growth over the last decade, making it Davis County's fastest-growing city. It more than doubled its population between 2000 and 2010 to more than 24,330 people today a trend that Carlson and others said had brought growing pains with it.
City council members Larry Shingleton, Brian Duncan and Craig Johnson did not answer several inquiries for comment.