Dutch Prime Minister Mark Rutte told the World Economic Forum in Davos that Europe has between six to eight weeks before it collapses due to the influx of refugees arriving from the Middle East.
Rutte warned that unless the EU gets a grip on the migrant crisis, the entire bloc will break up.
Meanwhile French prime minister Manuel Valls admitted the EU “could very well break up in a very short time”.
He warned the ongoing refugee crisis across Europe and the threat of Islamic State (ISIS) terrorism could spell the end of the political union on the continent.
Speaking at a summit of global elites in the exclusive Davos ski resort in Switzerland, the French politician suggested the EU had not been built to withstand “such powerful crises” of an unprecedented flow of migrants across the bloc’s borders or ISIS-inspired attacks.
Mr Valls described Britain’s possible exit from the EU at an upcoming referendum as a “tragedy”, while hoping a deal on the UK’s membership could be reached in February.
Having earlier thanked fellow EU member states for their solidarity in the wake of the Paris terror attacks last November, he said: “Europe may not have been conceived in order to face up to such powerful crises as that of the refugees or the terrorist menace.
“We will have to live for decades or for many years with this menace or this threat and that’s why it’s a war. There are many generations that will have to live with this and the crisis will have to be managed in north Africa and the Middle East.
He added: “We have to live with this it’s a part of our lives now. It’s a challenge and it’s a feeling history can be tragic and Europe could very well break up in a very short time. We have to be realistic.”
But despite his warnings over the current crises facing the EU, the French prime minister said solutions would be found in “more of Europe not less of Europe”.
Mr Valls also urged British voters to reject the chance to cut ties with Brussels, adding: “Seeing Britain leave the European Union would be a tragedy.
“We must do everything for Britain and the British people … to stay in the European Union.”
But Mr Valls warned Britain would not be able to remain an EU member “at just any condition”.
French president Francois Hollande reiterated his prime minister’s remarks later, as he warned David Cameron his ongoing renegotiation of Britain’s relationship with Brussels must respect the EU’s founding principles such as the free movement of people.
He also said the Prime Minister’s demands for EU reforms, on which he hopes to reach an agreement at next month’s summit of EU leaders, would not be allowed to interfere with greater integration between countries using the euro single currency.
Mr Hollande said: “I will be particularly vigilant that the euro zone can pursue its integration, for me that is the essential point.
“If Britain wants to go its own way within the EU we can allow it, but that cannot prevent the countries that want to go further in integration, monetary for example”.
Mr Rutte, who was speaking on a panel alongside Mr Valls at the World Economic Forum in Davos, also said he was “fairly optimistic” the EU could agree a deal on Britain’s membership in February although he added he was “not absolutely sure”.
Mr Rutte claimed Britain being outside the EU would be “worse off” and “won’t have the influence it has in the world it has today”.
He added: “Isn’t it strange to even debate a Brexit at a time when the world is facing all these huge issues and challenges?”
The annual Davos summit is often criticised for only being attended by globe-trotting elites and wealthy businessmen, while others wonder what it actually achieves.
But Mr Rutte urged those in the audience to intervene on the Brexit referendum and “don’t leave it only to politicians” to campaign for Britain to remain in the EU.