AhlulBayt News Agency - The French Foreign Office today warned that stadiums, bars and fan zones showing the matches could be targets for terror attacks.
Fans were warned to be vigilant during the tournament in France, which is on alert after Europol warned there was a 'high threat' of an ISIS attack.
Scotland Yard also revealed today that it has seen ISIS propaganda and talk of plots during the tournament, and the threat level remains 'severe'.
The news comes after a French terrorist planning 15 attacks during the Euros was arrested yesterday with a vast arsenal of weaponry - including 125kg of TNT and 5,000 rounds of ammo.
The right-wing nationalist Gregoire Moutaux also had two rocket launchers, five Kalashnikov assault rifles and more than 100 detonators when he was arrested on the Ukraine's border with Poland.
A source close to the investigation said he was 'armed to the teeth and ready to strike'.
The news came as French intelligence agencies said they were 'deeply concerned' about attacks from homegrown terrorists, after 16 Real Madrid fans were slaughtered in Iraq in May.
They said that the mass murder was considered 'a postcard' from ISIS to the West ahead of the tournament which kicks off in Paris Friday.
The host nation kick off at the at the Stade de France on, where two suicide bombers blew themselves up during the infamous Paris attacks in November that left 130 dead.
British counter-terrorism officers are playing 'a key part' in planning against potential atrocities at Euro 2016, Commander Dean Haydon said.
A police operation targeting 29 UK ports in the run-up to the tournament began on Monday, with trained spotters trying to detect football hooligans attempting to sneak out of the country.
Commander Haydon, the head of Scotland Yard's anti-terror squad, said: 'As we approach the Euros, any operation such as that in any country is clearly a concern.
'As you would expect, we are working with the French and other local police and security and intelligence agencies across the world to properly understand is there a threat to the Euros.
'Certainly we have seen propaganda, so-called Islamic State (IS) and potential talk of plots against the Euros, but we're working with all those various different agencies to police and make the Euros a safe event and a safe games.
'We're a key part of the planning. Although the ultimate policing of the event and the planning is for the French, we are all involved in properly trying to understand the threat, if there is one.'
He dismissed the threat of the far right on the UK mainland, adding: 'The general threat we’re seeing at the moment across Europe is certainly from IS, not the far right at all. We’re not seeing a threat there at all, we’re seeing it from IS and other terrorist organisations coming out of Syria.'
Currently 1,841 England fans and 86 Wales supporters are subject to banning orders that stop them travelling to the tournament.
Matches at Euro 2016 will be played across several stadiums and there are a string of fan zones for thousands of supporters.
Fan zones will also be set up in London, which will be policed 'normally', Mr Haydon said.
The advice issued today read: 'During Euro 2016, stadiums, fan zones, venues broadcasting the tournament and transport hubs and links represent potential targets for terrorist attacks.
'You should be vigilant at all times, especially in areas hosting Euro 2016 events, and follow the advice of local French authorities.'
Commander Haydon added: 'The threat level in the UK remains at severe, so an attack is highly likely - that has not changed. If we see increased intelligence coming out of France or anywhere in the world that suggests there's going to be an attack here then of course, through Cobra (emergency committee) and Government, we will review that threat level accordingly.
'There are different events taking place throughout London, there are fan zones, there are screens going up for people in crowded places and in parks to watch the football. Of course we've got a policing event around that.
'We are policing that as we would do normally and obviously keeping an eye on France.'
Prime Minister David Cameron chaired a meeting on Monday on preparations for the tournament.
A Downing Street spokeswoman said the French authorities 'have got an extensive security operation in place, with 77,000 police and gendarmes, 10,000 military personnel and a similar amount of security guards'.
She added: 'We are providing additional counter-terrorism and public order support to the French. That includes, for example, the deployment of additional police on trains into France and more UK Border Force outbound checks.'
A Foreign Office spokesman said: 'We have updated the travel advice to provide further information for fans on the risk of terrorism in France as they start to travel for Euro 2016.
'This is consistent with the advice we have already issued for France and is not in response to a new or specific threat or yesterday's arrest.
'The relevant UK authorities are in constant contact with the Euro 2016 organisers and local authorities. France has lots of experience of hosting large scale events and the authorities have undertaken extensive preparations for the tournament.'
'We have to be linked in with football police officers as well, the football policing of the event, and looking at threat and contingency planning in the event of an incident, and that’s why we’re working very closely with the French and we’ve got a variety of officers in France working with them to deliver a safe games.'
The news comes after it was claimed yesterday that up to 82 workers hired to bolster security at Euro 2016 are on French terror watch lists.
French intelligence chiefs have screened 3,500 staff brought in to ensure the safety of fans at the tournament, which begins on Friday when host nation France takes on Romania.
The 82 people highlighted on watch lists could 'by definition' either belong to a terror group or have a background of 'questionable behaviour or extreme beliefs on either the left or right', it was reported.
Europol director Rob Wainwright said last week he had 'no doubt' the football tournament would be a target for the terror group.
The U.S. government had earlier issued a travel alert to Americans, warning of the risk of potential attacks throughout Europe.
The State Department singled out the tournament, which will be held in France from June 10 to July 10.
Mr Wainwright, from Wales, said: 'I have no doubt that the Euros are on a potential target list for ISIS, for obvious reasons.
'That's a pretty obvious assumption. The threat is high, I think.'
But he said the the risk is 'not necessarily high' given the massive security operation set to be mounted by the French authorities.
Euro 2016 will take place amid an atmosphere of high alert following atrocities in Paris and Brussels.
Last November, 130 people were killed when terrorists launched co-ordinated attacks on the French capital, targeting bars, restaurants and the national stadium, the Stade de France.
Then in March, 32 people died when Brussels was hit by suicide bombings at the airport and on the Metro.
French authorities have extended a state of emergency until the end of the tournament, as well as the Tour de France cycling race, which will be held from July 2 to July 24.
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