With the polls 50-50 on the likely outcome of the referendum on 23 June, the German MEP has suggested those advocating the UK pulls out of the EU had lost touch with reality.
He said, "People who claim that nation states would do better to go it alone have lost touch with reality. Surely nobody really believes that, if our continent were to fragment, we Europeans, and our unique social model, could survive in an ever more globalised and interconnected world."
Schulz was speaking on Friday in the Vatican on the occasion of the award of the EU's Charlemagne Prize to Pope Francis.
Meanwhile, former UK Europe Minister Denis MacShane says a Brexit would harm efforts to tackle global warming.
The Renewable Energy Association recently polled its members on the EU referendum and the effects on their business. The majority of its members felt the UK would be less likely to meet its climate targets, renewable deployment would decrease, and expected their business to risk contraction if the UK left the EU
MacShane, who served under former UK Prime Minister Tony Blair, said, "Clearly one of the big EU achievements is to be a world leader on raising environmental standards. Air pollution and global warming do not respect national frontiers and a Brexit would weaken the EU overall efforts to raise environmental standard - in which UK ministers and officials working in Brussels and across the EU have a deal of influence. There is no doubt that Brexit would be a backward step for enforceable trans-frontier regulation in this key policy area."
However, his comments were rejected by the Leave campaign.
One of its leading proponents, Matthew Ellery, of the Get Britain Out group, also denied that a Remain vote is not looking more likely.
He said, "The polls, for what they are worth, are saying the vote is neck and neck, with the Leave campaign in the ascendancy, especially with those who are certain to vote. This is because those opposing the European Union are very passionate in defending the fundamental right of democracy and will do everything in their power to regain the ability to hold those who govern them to account. We at Get Britain Out totally oppose a second referendum, we hope the British people with vote to Leave and the Government will be forced to accept the result."
He also says that the economic evidence is not against the Leave campaign.
"Independent economic analysis, such as the research conducted by Open Europe, which is neutral in this referendum, has not supported the view that Remain is better for our economy. They claim Brexit could result in a boom for the UK economy. The economic impact will totally depend on the policies undertaken by our Government after Brexit.
"Leaving the EU will not solve economic problems; however it will give our elected representative the tools to fix it. Research conducted by pro-EU organisations and organisations which are funded by the EU isn't worth the paper it is written on."
Ellery said the key argument made by the Leave campaign, "which cannot be repudiated," is one of democracy.
He said, "The belief that our laws should be made by our elected representatives in Westminster and by the devolved assemblies, not by the unelected European Commission. This is a positive vision, unlike the unfounded negative arguments made by the Remain campaign."