Boris Johnson said he understood “people’s strength of feeling” about the ownership of football clubs and the anger which lay behind the pitch invasion at Old Trafford, as police said a 28-year-old man had been arrested over the incident.

Greater Manchester police (GMP) said six officers had been injured in Sunday’s protest when bottles and cans were thrown from the crowd, including one who required hospital treatment for a fractured eye socket, another with a face wound and one who was dragged and kicked.

The prime minister was responding to questions about the disruption which caused Manchester United’s Premier League game against Liverpool to be postponed and which has led to a police investigation.

“I don’t think it’s a good idea to have disruptive behaviour, demonstrations of that kind. But on the other hand, I do understand people’s strength of feeling,” he said during electoral campaigning in Hartlepool.

Fans broke into the stadium on Sunday and invaded the pitch in protest at the club’s owners, the Glazer family, while outside the ground bottles and barriers were thrown at police officers and horses.

GMP did not say which offence the 28-year-old had been arrested on suspicion of. The force said: “All available evidence is being urgently reviewed to identify both the organisers of this protest and those responsible for the officer assaults.” The officer who attended hospital has since been discharged.

The GMP assistant chief constable Nick Bailey said: “The behaviour shown at this protest was absolutely atrocious. Officers were just trying to do their job and facilitate a peaceful protest, however a number of those present became hostile and aggressive towards officers and forced entry to the football grounds, making it very clear that this protest was not peaceful and ruining it for the majority of protesters who had not intended for the protest to become violent.

“Our officers tried to engage with protesters but were met with violence and aggression, which resulted in enforcement action being taken. Enforcement will always be a last resort, but in these circumstances it was deemed necessary in order to maintain safety during a situation that was rising in hostility.”

Stu Berry, the chairman of the Greater Manchester Police Federation, which represents the force’s rank-and-file officers, said on Monday one of the injured officers was a constable with around 20 years’ service. He said: “He is incredibly lucky not to have lost the sight in an eye.”

While Manchester United was continuing to work with police to identify fans, PA Media said it understood the club was focusing its efforts on those who committed offences and that sanctions would not necessarily be applied to fans who merely entered the stadium or went on to the pitch.

“The club has no desire to see peaceful protesters punished, but will work with the police to identify those involved in criminal activity, and will also issue its own sanctions to any season ticket holder or member identified, per the published sanctions policy,” said a statement.

Under the club’s sanctions policy, damaging property or disorderly behaviour warrants a ban of one to six games, while abusive or aggressive behaviour towards staff, police or anyone else at work, or any other criminal activity can lead to indefinite suspension.

Speaking on Monday before Johnson’s comments, another member of the government also said the frustration felt by fans towards some football clubs had to be understood.

James Cleverly, a Foreign Office minister, said he could not condone the events at Old Trafford, but added: “We do need to understand the frustrations that fans have, not just with Manchester United, but with a number of clubs across the game.”

The postponement of the Premier League match added further uncertainty to United’s fixture list in a week when they are due to play the second leg of their Europa League semi-final with Roma, and is the most graphic illustration yet of the breakdown of trust between fans and owners.

About 1,000 protesters had gathered at Old Trafford by 1pm on Sunday holding anti-Glazer banners and chanting against the American family, whose longstanding unpopularity with supporters was elevated by their signing up to the now-defunct ESL. Another 200 gathered at the Lowry hotel in Salford where the United players were staying. GMP said officers “were met with hostility as flares were let off and bottles and barriers were thrown at police officers and horses”.