Police made nine arrests following Manchester United's 4-2 Premier League win over Leeds United during which a Manchester player appeared to have been hit by something thrown from the crowd, they said on Monday.

Second-half goals from substitutes Fred and Anthony Elanga earned Manchester United victory on Sunday in a red-hot atmosphere in Leeds and Elanga appeared to be hit by an object while celebrating Fred's goal.

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Manchester United and Leeds United have had a fierce rivalry over the years.

"There was no significant disorder but there were a few incidents in Leeds City Centre ahead of the game and some minor incidents throughout the game," West Yorkshire Police said in a statement.

"Officers were deployed in sufficient numbers to rapidly intervene to identify and arrest the people responsible and prevent any escalation in disorder."

"The majority of fans on both sides behaved appropriately throughout the match and there was no significant disorder, but we hope the early intervention and positive action ... will help send a very clear message," Deputy Chief Constable Russ Foster added.

Leeds United issued a statement saying they were reviewing CCTV footage of the match.

"... We will do everything possible to find those supporters who are throwing objects on to the field of play," a club statement said.

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"Any supporter caught throwing objects on to the pitch will be issued a lifetime ban from attending our fixtures."

According to media reports, the Football Association is aware of the incident involving Elanga and is looking into it, with Manchester United manager Ralf Rangnick and Leeds United boss Marcelo Bielsa condemning the supporters involved.

"Obviously things like that should not happen and I think ever more so in this game, the atmosphere was great at times we had to cool down," Rangnick said.

Bielsa said he had not seen the incident but said violence in football "should not be approved".