Labour will support the government in introducing prison sentences of up to 10 years for those who desecrate war memorials.
Shadow home secretary Nick Thomas-Symonds told Sky News his party was “willing to work with the government” on proposed new legislation.
Recent protests in London have seen the Cenotaph marked with graffiti, while on Saturday a man was photographed apparently urinating next to the memorial to PC Keith Palmer, the policeman killed in the 2017 Westminster terror attack.
A group of MPs will meet Justice Secretary Robert Buckland this week to discuss proposals to amend existing laws to make a provision about damage to war memorials.
The Sunday Telegraph reported Home Secretary Priti Patel and Attorney General Suella Braverman will also join the discussions with Conservative backbenchers.
The newspaper said one option being considered by ministers is to amend the Criminal Damage Act.
This would make war memorials exempt from a stipulation that damage amounting to less than £5,000 should be treated as a lesser offence and handled by a magistrates’ court.
Asked about the newspaper report, Mr Thomas-Symonds told Sky News’ Sophy Ridge on Sunday show: “I would support the government in creating a specific offence of protecting war memorials and I would be willing to work with the government on that.”
Appearing on the same programme, Chancellor Rishi Sunak said “one of the most distressing” aspects of recent protests was the treatment of memorials.
“I know many people, certainly MPs, have raised this issue,” he added.
“The justice secretary will be meeting with all those MPs, I believe this week, to discuss these matters further.
“But that was absolutely shocking scenes to see yesterday.”
Tory MPs Jonathan Gullis and James Sunderland, who served in Iraq, Bosnia, and the Falklands during his time in the British Army, have proposed a Desecration of War Memorials Bill.
The proposed legislation, aimed at enabling police and courts to more easily prosecute those who damage memorials, is due to be considered by the House of Commons on 23 June.
Mr Gullis recently wrote on his website: “Desecration of memorials that remember those who made the ultimate sacrifice so we can enjoy the freedoms we have today is repugnant”.
He added: “At present there is no specific law to protect these important monuments and unless £5,000 worth of damage is done, it is incredibly hard to prosecute.
“We sadly lack in this area compared to our Commonwealth friends.
“Therefore I will be putting forward this bill to bring about a clear custodial sentence and fine for such heinous acts.”
Charlie Gilmour, the son of Pink Floyd guitarist David Gilmour, was jailed for 16 months for violent disorder during the 2010 student protests in London.
He was photographed swinging from a Union flag on the Cenotaph.