Home Secretary Theresa May has confirmed there was "contact" between the Duchess of Cornwall and one of the protesters who attacked her car.
But she did not confirm reports the duchess was poked with a stick during student protests on Thursday.
The Commissioner of the Metropolitan Police, Sir Paul Stephenson, has spoken to Prince Charles about the incident.
Charlie Gilmour, son of Pink Floyd guitarist David Gilmour, was arrested on Sunday following the protests.
Police said a 21-year-old Sussex man was arrested on suspicion of violent disorder and attempted criminal damage.
The man was accused of damaging the Union flag on London's Cenotaph.
On Friday Mr Gilmour apologised for climbing on the Cenotaph during the protests.
Just before 1500 GMT a 17-year-old man handed himself in at a central London police station and was arrested on suspicion of violent disorder.
The police had issued images of 14 alleged rioters.
Several protesters launched an attack on a car carrying Prince Charles and the Duchess of Cornwall as it passed along Regent Street.
Their Rolls-Royce was kicked, splashed with paint and a window was cracked to chants of "off with their heads".
There were reports Camilla was poked with a stick, through one of the car windows as the royal couple made their way to the London Palladium.
Mrs May told Sky News: "I'm not sure about the term 'poked with a stick'. I understand there was some contact made.
"Again this is an incident that needs to be looked at by the Metropolitan Police. That is what they are doing. So we will very soon have the details of that.
"And obviously it will be for them to look at what happened and decide whether there are any lessons that need to be learned."
She said she had not considered offering her resignation over the incident and added: "Of course that's an incredibly regrettable incident that took place.
"We should praise the Prince of Wales and the Duchess of Cornwall for their response - they carried on with the engagement they were doing that evening so they didn't let down the people who were expecting them."
A Clarence House spokesman confirmed Prince Charles and Sir Paul spoke following Thursday's incident.
A Scotland Yard spokesman declined to confirm reports the commissioner apologised personally to the Prince.
There has been speculation in the wake of the incident that the Prince of Wales may trade in his Rolls-Royce for a more secure vehicle.
Mrs May said the Phantom VI might not be "appropriate" for the purpose any more.
The car was a gift from the Car Association to the Queen in her Silver Jubilee year of 1977, but Mrs May said: "One of the issues that may very well be looked at is the question of the appropriate transport that is used by the Prince of Wales and Duchess of Cornwall."
Prime Minister David Cameron has said protesters who engaged in violence should face the "full force of the law".
Ms May is due to make a statement on the tuition fees protests in the House of Commons on Monday.
Officers have reviewed hours of CCTV footage as part of their investigations into the disorder and have appealed for the public's help in identifying suspects.
Detective Chief Superintendent Matthew Horne said: "The vast majority of the people we are seeking are suspected of committing serious offences of violent disorder and criminal damage."
He added: "The rights of protest and expression are important to us all.
"However, people breaking the law, endangering those protesting peacefully and committing offences such as this are criminals."
Meanwhile, police have been accused of trying to stop civilians injured during the student protests being treated at the same hospital as officers.
Protester Alfie Meadows, 20, needed brain surgery after allegedly being hit with a police baton.
His mother Susan Matthews said police objected to him being treated at Chelsea and Westminster Hospital.
The student was treated there after a "stand-off" between police and medical staff, but was later transferred to Charing Cross Hospital where there is a specialist brain injuries unit.
A spokesman for Chelsea and Westminster Hospital confirmed a decision had been taken to treat officers there and civilians in other hospitals.
But he said because so many protesters ended up being injured some were treated at the hospital.
Scotland Yard has launched a "major criminal investigation", called Operation Malone, into all the tuition fee protests held from 10 November, when students stormed Tory headquarters in Millbank, up to Thursday's demonstration in Parliament Square.
A total of 175 people were arrested during the four demonstrations, including 34 who were detained on Thursday.
Police are urging people who can identify any of the suspects whose pictures it has released to call 020 8358 0100 or Crimestoppers on 0800 555111.