Borders between countries will become "irrelevant" by the end of the century, the shadow chancellor has suggested.
John McDonnell said it is inevitable that there will eventually be open borders, warning that people are already "ignoring" boundaries that currently exist.
Meanwhile, Mr McDonnell also said the UK should be doing more to help the millions of migrants arriving in the European Union.
The Labour frontbencher delivered a speech in 2013 in which he suggested borders could become a thing of the past.
Appearing on the BBC's Sunday Politics programme, Mr McDonnell was asked to elaborate on that suggestion.
"Inevitably in this century we will have open borders," he said.
"We are seeing it in Europe already.
"The movement of peoples across the globe will mean that borders are almost going to become irrelevant by the end of this century so we should be preparing for that and explaining why people move."
Mr McDonnell stressed the need to deal with the causes of mass migration: Poverty, conflict and climate change.
"In that way we can deal with the reality of the world which means that people aren't forced to move but there will be movement," he said.
When asked whether he believes there will one day be totally open borders with no controls, he said: "I think at the end of this century that's what will occur.
"We are seeing people ignoring borders already as they fly from Syria."
Current estimates suggest close to 4 million migrants will arrive in the EU between 2015 and 2017.
Mr McDonnell was asked if the UK should take its fair share of those people.
"I think we should," he said.
"I think we should cooperate with others and carry the burden because we are seeing, as in the refugee crisis, the majority of Britons want us to rise to that and ensure that we assist others and that others aren't suffering and that we don't stand on one side while people suffer."
Mr McDonnell was unable to say how many people he would like to see the UK help.
He also suggested the UK should be a part of the EU's refugee quota scheme.
"I think we should be doing more in terms of assisting the refugees coming in through Syria," he said
Tim Farron, the leader of the Liberal Democrats, told Murnaghan on Sky News the UK should take its "fair share" of migrants.
He said: "I want Britain to take its fair share and to engage with our European partners. Then we could come up with ways of having safe routes.
"There must be a way of dealing with this that doesn't involve turning our backs on refugees as well as our partners in Europe.
"The reality is we are not going to turn off the tap. Most of them are not economic migrants.
"The UN is clear that 94% of those going to Lesbos were refugees. We should open our arms to them."