"We should be opening the extern borders – I mean the EU's external borders – in a coordinated way," the minister told the Ziniu Radijas radio station.
"There's an understanding that we shouldn’t do so (open the external borders) until June 15. And that may be extended further, I'd predict, until the end of June," he added.
Unlike the initial response to the coronavirus pandemic, EU member states should coordinate their exit from the crisis and preparations for possible future challenges, according to Linkevicius.
Meanwhile, the EU's internal borders are already opening up to travelers, and the Baltic countries are a good example of this, Linkevicius said.
"Latvians, Estonians and we have created that travel bubble, a move that has drawn attention from global news agencies, not only those of Europe," the minister said.
"Poland is moving closer to (joining) us – I've just recently discussed this with my (Polish) counterpart – and I believe Finland is thinking about it, too. And that bubble will eventually expand into a Schengen bubble," he added.