Both the Prime Minister and the Home Secretary have expressed concern about the prospect of further pro-Palestine protests next Saturday during Armistice Day.
Although demonstration organisers in London have pledged to avoid the Whitehall area where the Cenotaph war memorial – the focus of national remembrance events – is located, Suella Braverman has warned that anyone who vandalises the Cenotaph, should be arrested.
Speaking to Sky News's Sunday Morning With Trevor Phillips programme, Mr Dowden said: "I think that at a time that is meant to be a solemn remembrance of the sacrifice of previous generations and upholding our British values, I think the police need to think very carefully about the safety of that demonstration, namely whether it could spill over into violent protest and the signal it sends particularly to the Jewish community.
"Now, I understand that the Met Commissioner continues to keep it under review and I think that is appropriate."
Asked whether he was sending a signal to the police that the march currently planned for November 11 should be banned, Mr Dowden said: "The police are operationally independent.
"But I do have very grave concerns about that march, both in terms of how it sits with acts of solemn remembrance and the kind of intimidation that is being sent out by the chants and everything else that goes on at those marches.
"I think it is right that it is the law of the land that the police are operationally independent. But I think it is important that they consider those factors, yes."
Mr Dowden's comments come after 29 people were arrested at a pro-Palestinian rally in central London on Saturday.
Thousands of protesters had marched on Trafalgar Square to demand a ceasefire and an end to Israel's bombardment of the Gaza Strip in response to Hamas' brutal attack on October 7.
Commander Karen Findlay said that demonstrators had also injured four officers by throwing fireworks in their direction.
Meanwhile, the British Transport Police (BTP) said they were investigating footage that appeared to show a crowd of people in a Tube carriage chanting "from the River to the Sea" and "intifada, revolution".