The duo were involved in a heated exchange on Friday that led to police being called to Swansea's training ground.
However, a club statement confirmed no action was taken by police and both Monk and Flores have now presented a united front, denying reports that the Spaniard had threatened his team-mate with a brick.
Swansea club captain Monk said: "I have been playing in the professional game for 20 years and training rows are nothing new in a competitive and pressurised environment.
"Recent media reports have blown everything out of proportion. Yes, we had words, but at no time was I threatened with a brick by anyone.
"Chico is a team-mate and we stick together for the betterment of Swansea City and the fans. That it is the case throughout the squad.
"The matter has been resolved and we all remain united, whatever nationality we may be, because we wear the same club colours and that is the most important thing.
"We are a tight-knit group; we always have been and always will be."
Flores echoed Monk's comments, claiming their fall-out was an example of typical frustration when a club is not performing on the field, with Swansea having gone eight Premier League games without a win.
"It was just an argument between team-mates as can happen sometimes in a training session or in any changing room of any football team…nothing more," added Flores.
"I did not threaten anybody in any moment and even less with a brick. I consider myself a respectful person and a good team-mate who likes unity and closeness and I help create a good atmosphere around my team-mates.
"My relationship with Garry Monk has always been fantastic and still is...any person that is involved in the business of football knows that these small arguments regularly happen in training sessions and even more when things are a bit more tense than normal for not getting good results.
"So I just want all you fans to know that Garry and I are two very committed players for Swansea City and it was nothing more than just a silly argument - nowadays things get blown out of proportion in the press and on social networks."
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