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Suarez, who has served two previous suspensions in his career for biting opponents, was not punished by Mexican referee Marco Rodriguez despite Chiellini's protests. The Italy player pulled his shirt from his shoulder in order to highlight the bite marks to the referee.
Moments later, Uruguay took the lead against Italy, who earlier had Claudio Marchisio sent off, through a Diego Godin header and went on to win 1-0, qualifying for the round of 16 at the expense of their opponents.
Suarez did not explicitly confirm or deny that he bit the Italian in the match said that Chiellini barged into him during their clash.
"These are just things that happen out on the pitch," Suarez said. "It was just the two of us inside the area and he bumped into me with his shoulder, and that's how my eye got like this as well. There are things that happen on the pitch and you should not make such a big deal out of them."
After the match, Juventus defender Chiellini called Suarez's action "a disgrace" on Sky Sport Italia and called for FIFA action.
"Suarez gets away with whatever he wants because FIFA want the top players involved," Chiellini said. "He bit me, and the sign is there. Now [FIFA] have got to have the courage to take action."
FIFA regulations allow Suarez to be punished retrospectively and it has said it "will gather all the necessary elements in order to evaluate the matter."
Speaking from his home in Northern Ireland, FIFA vice president Jim Boyle said on British television that Suarez had let himself down again.
"There is no doubt Luis Suarez is a fantastic footballer but, once again, his actions have left him open to severe criticism," said Boyle, who is also chairman of the FIFA referees' committee. "FIFA must investigate the incident seriously."
Suarez did not appear to be asked about the incident when speaking to reporters following the win.
"The truth is that the work which the team put in was incredible," the striker said, according to Ovacion. "After having started the group badly against Costa Rica, the best we deserved was this, and we showed why we are at this World Cup.
"I was relaxed because I knew we would have chances. Then the goal came. Uruguay is in party mood -- we have qualified and now this moment must be celebrated, as we will then have to think about our next opponent."
Uruguay coach Oscar Tabarez said he would like to see replays before commenting on Suarez, but indicated that the team would stand by their striker.
"I did not see the incident," Tabarez said. "I will not make any more comments about it. Luckily, we've played many matches without Suarez for qualifiers and, for us, he is a very important player and important person within the group. We will see how to defend him. This is a football World Cup, not about cheap morality."
Suarez previously served a 10-game ban for biting Chelsea defender Branislav Ivanovic while playing for Liverpool in the Premier League as well as serving a seven-game ban for a similar incident while with Ajax.
Suarez, who was Ajax captain at the time, bit PSV Eindhoven midfielder Otman Bakkal's shoulder during a 0-0 draw in 2010.
During the game against Chelsea, a 2-2 draw in April 2013, the incident with Ivanovic was not seen by referee Kevin Friend and Suarez was banned as a result of retrospective action.
Tabarez said the media's focus on Suarez is overblown.
"Besides the mistakes he might have made, he is the target of the media that give him much more coverage to the alleged things he's done," Tabarez said. "It seems to me that there is animosity against him and if we see errors, we are the first ones who see that with a positive spirit and for this player not to make these mistakes again.
"I'm under the impression that there are always people waiting behind the tree and waiting for something to happen."
The forward has been linked with a move away from Liverpool this summer with Barcelona and Real Madrid rumoured to be interested in signing him.
He signed a four-and-a-half year contract with the club in December 2013 in a bid to ward off interest from rival clubs, but after scoring 31 Premier League goals and helping Liverpool mount an unlikely challenge for the Premier League his profile rose.
Suarez also won a host of awards for his displays last season including the PFA Players' Player of the Year, despite missing the first four games of the campaign as a result of his ban for biting Ivanovic.
Speaking about his past, Suarez told The New York Times in an interview in May: "Obviously, it's not the most attractive image that I can have for myself. But that's not what I want to be remembered for. I want to do things right. I really, really do."
WATCH: Could Suarez be in trouble for apparent bite?
Uruguay's Luis Suarez appears to bite Italy's defender Giorgio Chiellini in their Group D encounter.
Bad boy Suarez at it again
Liverpool and Uruguay forward Luis Suarez is at the centre of yet another biting incident after apparently biting Italy's Giorgio Chiellini.
FIFA to come down hard on Luis Suarez?
The Last Call crew discuss the measures that FIFA may take against Luis Suarez following his biting incident in Uruguay's 1-0 win over Italy.