In a stinging attack he added that Vitoria, who won the Portuguese Cup with unfashionable Vitoria Guimaraes in 2013, was "not my colleague" and did not have what it took to be involved in coaching.
League leaders Sporting, who won 6-0 at Vitoria Setubal on Wednesday, are four points clear of Jesus' old club Benfica who beat Maritimo by the same score, and Porto.
"I don't consider him to be a coach, he is not my colleague," said Jesus dismissively in a post-match news conference. "To be a coach you have to have a lot more (than he's got)."
Jesus, who has a reputation for being a testy character, left Benfica after six years to take over at arch-rivals Sporting at the end of last season in a move that stunned Portuguese football.
Sporting have won all three meetings between the teams since then, in the Supercup, the league and Portuguese Cup, heaping the pressure on Vitoria.
Jesus has made frequent references to his former club, at one point saying Vitoria was a "victim" of his past success at Benfica that included three league titles and two Europa League finals.
Vitoria stoked the rivalry on Tuesday when he said there were "two coaches obsessed with Benfica" in a clear reference to Jesus.
"I'm obsessed with Benfica just as I'm obsessed with all our rivals," said Jesus. "That's why we've beaten Benfica three times this season."
Vitoria declined to reply. "I don't want to be involved in a soap opera," he said.
The president of the Portuguese coaches' association appealed for calm from both men.
"All I can ask for is a little more respect for the profession and for the clubs themselves," said Jose Pereira. "It doesn't make sense for two top-level coaches to behave like this."
(Writing by Brian Homewood; Editing by Tony Jimenez)
