The Met Police was urged to “act” over “unacceptable” language used at a trans rights protest in London.
Seven statues in the city centre were also damaged during the demonstrations.
One placard at the protest in Parliament Square over the weekend reportedly showed an illustration of gallows alongside a slogan suggesting “the only good Terf (trans-exclusionary radical feminist)” is a hanged one.
Education minister Stephen Morgan told Sky News: “It’s completely unacceptable language to be used, and obviously any matters that break the law should be reported to the police, and hopefully police action is taken.”
Equalities minister Bridget Phillipson condemned the "completely unacceptable" scenes at protests following the Supreme Court ruling on gender.
She told ITV's Good Morning Britain: "What we have seen in recent days, where it comes to defacing of statues, some pretty terrible placards that have been displayed in protests around the country.”
Police have already launched an investigation after seven statues were daubed with graffiti before thousands of trans rights protesters marched through central London.
The Metropolitan said its officers were in Parliament Square at the time, but did not witness the “criminal damage” take place.
The area was densely populated with thousands of supporters who gathered for what was billed as an “emergency demonstration” days after a Supreme Court ruling on the definition of a woman.
“Fag rights” and a heart were painted on the banner held by suffragette Millicent Fawcett, and “trans rights are human rights” was sprayed on the pedestal bearing a memorial to South African military leader and statesman Jan Christian Smuts.
The square is home to 12 statues of political figures including Winston Churchill, Abraham Lincoln and Mahatma Gandhi.
No arrests have been made, but officers are investigating, Scotland Yard said.
Chief Superintendent Stuart Bell, who was leading the policing operation for the protest, said: “It is very disappointing to see damage to seven statues and property in the vicinity of the protest today.
“We support the public’s right to protest but criminality like this is completely unacceptable.”
Officers are also investigating reports of offensive placards but to date the images and signs were said to be from historic events, did not take place in London, or do not constitute a criminal offence.
Available footage of the protest is being reviewed and action will be taken, say police, if there are signs displayed that breached the law.
Activists at the demonstration demanded “trans liberation” and “trans rights now”, with some waving flags and holding banners as they marched towards St James’s Park.
This means transgender women with a gender recognition certificate can be excluded from single-sex spaces if “proportionate”.
The Government said the unanimous decision by five judges brought “clarity and confidence” for women and service providers.
The ruling means trans women cannot use single-sex female toilets, changing rooms or compete in women’s sports, according to the head of Britain’s equalities watchdog.
Ms Phillipson said the Supreme Court ruling meant service providers “can now operate with absolute confidence in delivering single-sex spaces for biological women”.
She told BBC Breakfast: “I do welcome the clarity that the Supreme Court judgment has brought in this area, making clear that biological sex is the basis on which single-sex spaces are provided.”
She said there would be more guidance for schools on gender-questioning children and “the heart of everything we do has to be about making sure that children’s wellbeing is supported, but also that school leaders in particular have the clarity and guidance that they want”.
