Donald Trump's state visit to the UK, which could take place in June, is likely to cost the police millions of pounds, Sir Bernard Hogan-Howe said.
Speaking on LBC, the Metropolitan Police Commissioner said there were already "some concerns" about potential protests but that assessments were continuing.
He said: "At the moment, of course, people are concerned that there might be lots of protests - there have been already.
"So no doubt as the days pass we will make assessments for what is going to happen."
Mr Trump's anticipated visit to the UK has caused outrage after he signed an executive order introducing a 90-day travel ban on residents from seven predominantly Muslim countries - Iraq, Syria, Iran, Sudan, Libya, Somalia and Yemen - to stop "radical Islamic terrorists" from coming to America.
More than 1.8 million Britons have signed a petition calling on Theresa May to rescind the invitation of a state visit.
A Parliamentary debate on the matter is due to take place on February 20.
On Saturday up to 40,000 people are believed to have taken part in demonstrations across the country in protest at the proposed visit.
Sir Bernard added: "We cannot definitely say there's going to be huge amounts of problems. I think we have got some concerns already; no doubt we will put a lot of officers out there and keep people safe to make sure that everything goes well.
"And if it is a few thousand officers, obviously it will cost quite a bit of money.
"I would think it is going to be the odd million but I can't be too precise."
Sir Bernard said he thought the plan was for Mr Trump to visit around June but he was not sure of exact dates. However Parliament will be in recess from May 25 to June 5.
"We are just waiting to hear all the details be fleshed out.
"State visits, usually there are two a year, and usually we get about six months' notice, but occasionally it has been far shorter notice than that and we have just got to get on and do it," said Sir Bernard.
The Prime Minister invited the American president to visit Britain later this year during a recent trip to the White House.
Controversy over the potential visit has also seen MPs call for a vote of no confidence in Speaker John Bercow who said Mr Trump should not address Parliament.
On Monday in the Commons, Mr Bercow appeared to brand the US president "racist" and "sexist" and said Mr Trump's travel ban meant he was "even more strongly" opposed to an invitation.