Officers are guarding the Rochdale Cenotaph after two incidents at the war memorial, Greater Manchester Police (GMP) have said.
Police Community Support Officers have been stationed by the cenotaph, which the force said is “currently a crime scene”.
An incident on Monday led to two teenagers, who cannot be identified for legal reasons, being charged with intentionally or recklessly causing public nuisance.
But the response to the second incident, which was reported shortly after 4pm on Tuesday, is ongoing, police said.
GMP did not give any further details.
The Rochdale memorial was designed by Sir Edwin Lutyens, who also designed the Cenotaph on Whitehall, which is the site of the National Service of Remembrance every November.
The central London memorial has featured in wider debate about whether a pro-Palestinian march in the city on Saturday should go ahead, with organisers pledging to avoid the war memorial.
The Metropolitan Police have urged protest organisers not to hold demonstrations on Armistice Day or Remembrance Sunday amid concerns about breakaway groups causing violence.
Chief Superintendent Nicky Porter, GMP Rochdale district commander, said: “We join communities across Rochdale in being deeply saddened by the incidents at the Cenotaph – the memorial is a particularly poignant reminder of those who have given their lives to our country, particularly at this time year.
“We will not tolerate the criminal disrespect of the town’s Memorial Gardens and I hope the action we have already taken in response to these two incidents reassures our communities of that.”
She continued: “Whilst the area is regularly monitored by CCTV operators and passing patrols, the partnership is working to sustain increased protection at this time.
“We have Police Community Support Officers at the scene at the moment and we will be looking to put lasting measures in place over the coming hours and days.
“We don’t underestimate the impact these events will have on our community of veterans, and I will be personally engaging with them and other community groups throughout this week.”
Anyone with information about Tuesday’s incident in Rochdale is asked to contact GMP quoting 1294 07/11/23 or Crimestoppers anonymously on 0800 555 111.