Urgent improvement in security is needed at Calais following the death of a migrant in the latest incursion at the Channel Tunnel, the Government said.
Home Secretary Theresa May said both the Government and Eurotunnel needed to work quickly to address the issue.
She made the comments as the operator said it has blocked more than 37,000 people attempting to cross in to the UK this year.
Speaking at the Home Office, Mrs May said: "A number of people have come through.
"We will be dealing with anybody's asylum claim in the normal way as we always do.
"But crucially what we are looking at now is improving security at the railhead at Coquelles, so we can ensure people are not trying to come through the tunnel.
"That means some urgent work in government but also with Eurotunnel, and Eurotunnel has a role to play here in the measures they themselves put in place to protect their trains."
However, a spokesman for Groupe Eurotunnel, which manages and operates the Channel Tunnel, said that since the arrival of migrants in the area around Calais, it has invested more than 160 million euro (£113 million), including 13 million euro (£9.2 million) in the first six months of 2015, in physical resources - fences, cameras, infra-red detectors - and personnel.
He added: "These considerable investments have already been followed in the second half of the year with new fencing around the platforms. Security patrol staff has been doubled to reach 200 employees, including sniffer dog patrols.
"To support the efforts of law enforcement in the Calais area, Eurotunnel has also provided buses to the authorities to enable them to remove any migrants intercepted."
The spokesman also said that Eurotunnel has kept the Intergovernmental Commission for the Channel Tunnel and authorities informed, over several months, about the "explosion" in the number of migrants present in Calais.
"The continuous pressure exerted every night is above and beyond that which a concessionaire can reasonably handle and requires a constructive and appropriate response from the governments," he added.
Speaking after chairing a Cobra meeting Mrs May said the Government was pressing for rapid installation of the new security fencing at Coquelles.
When asked if the military should be used, she replied: "This is about ensuring we get that security fencing up, it's about working with Eurotunnel to ensure we have got the best measures in place."
She added: "The key thing is to make sure we have got the security right at Coquelles and ultimately actually the answer to this problem is to ensure we are reducing the number of migrants who are trying to come from Africa across into Europe, that we break that link between making that dangerous journey, as it often is for people, and coming to settle in Europe.
"We do that by working with countries upstream, the work we are going to be doing with the French on returning people to West Africa and also on dealing with the criminal gangs that are making a profit out of people's misery."
Mrs May said the Government was working "very constructively" with their French counterparts.
She added: "We are working very hard with the French authorities and also with Eurotunnel to ensure we are able to increase the security at the railhead at Coquelles so we don't see people coming through the tunnel.
"Every effort is being put into that, a number of measures are now being discussed that have come out of the Cobra meeting today."
French Interior Minister Bernard Cazeneuve said that France would be reinforcing the means given to securing the border and the Eurotunnel site.
He also confirmed that two mobile units, or 120 additional police staff, will be "temporarily deployed in Calais in order to contribute to the security of the site".
Mr Cazeneuve also called on Eurotunnel to address security issues, adding: "In Calais, the state hasn't stopped assuming its responsibilities of maintaining public order, dismantling (immigration) networks, keeping foreigners without papers away, and putting into place humanitarian solutions for migrants and asylum seekers.
"Eurotunnel needs to also assume its responsibilities, notably regarding security," he told a press conference.
It was also announced that the total number of migrants who have died trying to cross the channel since June 26, has risen to nine.
Kent Police said Operation Stack - where freight traffic is parked on the M20 when cross-Channel crossings are disrupted - is expected to last into the weekend.
Sailings from the Port of Dover continued, with P&O Ferries running full services to Calais and DFDS operating a full schedule to Dunkirk and Calais.
The port said: "The port and the ferry operators are together working hard to serve all customers travelling to and from the continent. We apologise for any delays or inconvenience as a result of traffic congestion."
Kevin Hurley, the police and crime commissioner for Surrey, called for Gurkha soldiers based at Shorncliffe barracks in Folkestone to be deployed to protect Britain's border.
He said: "I am increasingly frustrated by the huge numbers of illegal migrants who jump out of the backs of lorries at the first truck stop – Cobham Services in Surrey – and disappear into our countryside. There were 100 in the last month alone.
"With ongoing cuts to police funding, year on year, it is hard enough to maintain regular policing, let alone the new demands around child sexual exploitation, cyber crime and domestic abuse, without also having to deal with desperate, homeless and penniless migrants as well.
"Of course, I realise that the root cause of this tragic migration is the appalling environments these people leave behind.
"They take enormous risks because they can see no other alternative. But, while the UK and French governments decide their next prevention strategy we, the British police, have to deal with the immediate problem.
"The Gurkhas are a highly respected and competent force, and are just around the corner. They could help to ensure that our border is not breached."
The UN High Commissioner for Refugees' representative in France, Philippe Leclerc, said the French authorities should do more to encourage migrants to claim asylum there. Around 50% of the 750 who have done so since November have got refugee status or international protection in France, he said.
Mr Leclerc told BBC Radio 4's World at One: "It's important that resources are increased to deal with asylum, and that asylum in France remains a credible alternative to crossing the Channel ... The effort has to continue on the part of the French to offer that opportunity."
Most of those in Calais are fleeing violence in countries like Syria, Eritrea, Somalia and Afghanistan and were among an estimated 200,000 who have crossed the Mediterranean to Italy and Greece in recent months, he said.
He added: "What we have seen is that many of the migrants do not in the beginning have the idea of travelling to the UK - only a minority of them do."
Former French minister Xavier Bertrand, who is standing for the Calais area in upcoming regional elections, told the programme that the UK needs to "do more" to resolve the situation.
"The English need to understand that having their border situated in Calais causes an enormous problem," said Mr Bertrand. "I'm urgently calling for an exception French-British summit so we can solve these problems ... The true question is where do you locate the English border - in England or in France?"
Mr Bertrand said France and Britain could work together on sea patrols to prevent migrants leaving Libya by boat. And he said it should be made more difficult for illegal migrants to work in the UK: "In England, you are able to work without papers easily. That's why they want to come to England. You don't need an identity card to live in England, that's why English employers use immigrants and why we've got this particular problem in Calais."
But Conservative MP Tim Loughton, a member of the House of Commons Home Affairs Committee, said: "What the French are trying to do - and the French are culpable to a much larger degree - is trying to make a European problem a British problem. If they can get it off their shores and onto ours, it's much less of a problem for them.
"There really is no justification for the French to allow 5,000 people with little grounds for being in the UK to gather at Calais and allow them to be there, and when they are detained for trying to get into Eurotunnel they are let go two miles out of the town, so they can try again and again. The situation will not improve while that nonsense goes on."