Sir Mark Rowley, the Metropolitan police commissioner, has said officers should not be “policing toxic culture wars debates” as the Father Ted creator Graham Linehan vowed to sue after his arrest over social media posts.

Rowley said “policing has been left between a rock and a hard place by successive governments”, with the law offering officers no option but to investigate Linehan’s tweets.

The 57-year-old was arrested by five armed officers from the Met as he got off a flight on Monday at Heathrow airport after arriving from Arizona.

Linehan was arrested for allegedly inciting violence and was detained by officers, who are routinely armed at the airport.

In one of the three tweets cited by the police at the point of arrest, Linehan had written: “If a trans-identified male is in a female-only space, he is committing a violent, abusive act. Make a scene, call the cops and if all else fails, punch him in the balls.”

In his statement, Rowley said the officers had reasonable grounds to believe an offence had been committed under the Public Order Act but that he understood the concerns raised.

“While the decision to investigate and ultimately arrest the man was made within existing legislation – which dictates that a threat to punch someone from a protected group could be an offence – I understand the concern caused by such incidents given differing perspectives on the balance between free speech and the risks of inciting violence in the real world,” he said.

“Most reasonable people would agree that genuine threats of physical violence against an identified person or group should be acted upon by officers. Such actions can and do have serious and violent real-world implications.

“But when it comes to lesser cases, where there is ambiguity in terms of intent and harm, policing has been left between a rock and a hard place by successive governments who have given officers no choice but to record such incidents as crimes when they’re reported. Then they are obliged to follow all lines of inquiry and take action as appropriate.

“I don’t believe we should be policing toxic culture wars debates and officers are currently in an impossible position. I have offered to provide suggestions to the Home Office on where the law and policy should be clarified.”

In comments that echoed those of the health secretary, Wes Streeting, earlier on Wednesday when he proposed a change in the law, Rowley added that he was ready to test a new approach “within a matter weeks”.

Rowley said: “Greater clarity and common sense would enable us to limit the resources we dedicate to tackling online statements to those cases creating real threats in the real world. If agreed, we could be ready to test new approaches quickly, within a matter of weeks.

“As an immediate way of protecting our officers from the situation we find ourselves in today, we will be putting in place a more stringent triaging process to make sure only the most serious cases are taken forward in future – where there is a clear risk of harm or disorder.

“But officers across the country will have to make similar decisions in future unless the law and guidance is changed or clarified. I hope to see this happen without delay so policing’s focus can be squarely on tackling priority issues like street crime and serious violence.”

Keir Starmer told the House of Commons on Wednesday that he believed the police should be able to focus on the most consequential issues.

He said at prime minister’s questions: “The commissioner has put out a statement in relation to the particular case this morning. I’ve been clear throughout that we must ensure the police focus on the most serious issues and the issues that matter most to our constituencies and all communities, and that includes tackling issues like antisocial behaviour, knife crime and violence.”

Speaking before a congressional committee in Washington, Reform’s leader, Nigel Farage, repeatedly cited the arrest of Linehan as what he called an “awful, authoritarian” situation for free speech in the UK.

Shami Chakrabarti, the former shadow attorney general and director of Liberty, said there were issues around free speech but there must always be limits.

She said: “Our society has become both polarised and illiberal, and public order laws have mushroomed in a vague and ad hoc way that is open to abuse.

“But inciting violence must always be a crime in a civilised society. Trans people are an especially vulnerable group who are now routinely subjected to threats of violence.”

Linehan is best known as the co-writer of the Father Ted comedy series and has been vocal about trans issues on social media.

The Guardian understands the Met is now talking to the Crown Prosecution Service, which decides whether criminal charges should be brought.

Writing on Substack, Linehan said he intended to sue the Met for wrongful arrest and breach of his human rights with the support of the Free Speech Union (FSU), which campaigns for the protection of freedom of speech.

Linehan said: “This was a horrible glimpse of the dystopian clown show that Britain has become. The FSU will support me by providing lawyers to advise on a claim against the Met police for wrongful arrest and wrongful imprisonment in the hope that no one else is treated like a terrorist for speaking their mind on social media.”

He said that after questioning by police his blood pressure “was over 200 – stroke territory” and that he was taken to hospital and kept under observation before being discharged and released on bail.