Four-times World Player of the Year Lionel Messi shot back angrily Sunday at rumours that he could leave Barcelona after clashing with coach Luis Enrique and the club's board.

The Argentine was in top form with a goal and two assists as the Catalan giants ended and unsettling week off the field with a crucial 3-1 win over La Liga champions Atletico Madrid.

"I have never demanded anything to ensure that I stay because I have never had any intention of leaving," he told Barca TV after Sunday's match.

"I have heard it said that my dad has spoken to Chelsea or Manchester City. It is all lies.

"I have taken this chance to deny it so that everyone knows the truth."

Messi had missed training on Monday, citing a stomach bug, after being left on the bench by Enrique for last weekend's 1-0 defeat to Real Sociedad.

And he sent the rumour mill into overdrive later in the day by following Chelsea and two of their players Thibaut Courtois and Filipe Luis on social media site Instagram.

Sources in the Catalan press then claimed Messi had met with Barca president Josep Maria Bartomeu in midweek to ask for the former Barca captain Enrique to be replaced as coach.

"I am grateful to be able to give my version of events," he said.

"It hurts me because it comes from here, from Barcelona, from people that love the club, or say they do. It doesn't come from Madrid like it has in the past.

"It is not good that they look for rivalry between Luis Enrique and I because there isn't any," Messi added.

"We need to be more united than ever, the fans and us. We have an important six months ahead to achieve good things for us and for the club."

Any doubts over Enrique's job in the short term were blown away by arguably his side's best performance in his seven-month reign.

Messi teed up Neymar to slot home the opener after 12 minutes and then repeated the trick to allow Luis Suarez to register just his second La Liga goal.

The Argentine inadvertently handed Atletico a route back into the game when deemed to have brought down Jesus Gamez inside the area on the hour mark and Mario Mandzukic slammed home from the penalty spot.

Messi made amends when he slotted home the clinching goal from close range three minutes from time to move Barca back to within a point of Real Madrid at the top of La Liga.

"This win has a special value because it is against a direct rival for the league," Suarez said.

"At the moment the self-confidence in the team is good. This win will gives us a big boost because it came against Atletico Madrid.

"It is spectacular to play with Messi and Neymar, just like the rest of my team-mates. We have achieved a great victory."