Northern Irishman Boyce, Britain's representative on Fifa, described Suarez's clear dive against Stoke as "nothing less than cheating" and said simulation was a "cancer" in the game.
That prompted the Uruguayan Football Association (AUF) to write to Fifa defending their player and demanding Boyce be referred to the governing body's Ethics Committee.
And Suarez, who played for his country in last night's 3-0 World Cup qualifying defeat to Argentina, has now has his say.
In an interview on Argentinian radio, quoted in The Sun, the 25 year-old said: "This guy (Boyce), I've no idea who he is.
"I don't know why he has been talking about me. He certainly can't be well-known and he wants to get publicity.
"Let him carry on talking. My job is to play football and to try to do so in the best way possible.
"What he has said does not affect me. I am not interested in what he has to say.
"It's been important to have the support of the Uruguayan FA and the people."
Suarez has always been a controversial figure, with the diving discussion adding to last season's race row with Patrice Evra, for which he was banned for eight matches.
And he said: "I have lived through a lot in the past year, with people saying things about me, but I have continued playing and proving my job is what happens on the pitch."
The AUF's letter, signed by the organisation's president Sebastian Bauza and general secretary Anibal de Olivera, described Boyce's remarks as "at odds with the principles of world football governing."
It continued: "The code of ethics of Fifa, in its article three, clearly states: 'Officers should be aware of the importance of their role and the obligations and responsibilities that entails'.
"Deliberately ignoring his position and role, Mr Boyce has referred specifically to a football player, encouraging and provoking hostility towards him."
The letter also included a list of six steps the AUF want Fifa to take, including withdrawing their confidence in Boyce, referring him to the ethics committee and expressing their regret to Suarez.
Boyce was talking earlier this week as he called for football associations to take retrospective action against players who dive.
Boyce said: "I have seen several incidents recently, and I watched the latest Suarez incident two or three times, and to me it is nothing less than a form of cheating.
"It is becoming a little bit of a cancer within the game and I believe if it is clear to everyone that it is simulation then that person is trying to cheat and they should be severely punished for that.
"It can be dealt with retrospectively by disciplinary committees, and it is done so in some associations, and I believe that is the correct thing to do."