It includes citizens from Japan, South Korea, New Zealand, Australia and Canada who will be given the green light.
On Monday, Prime Minister Jacinda Ardern warned that those planning to leave the country for "non-essential" reasons during the Covid-19 pandemic might be left picking up their isolation or quarantine bill on return.
The EU Council said that member states "should not decide to lift the travel restrictions for non-listed third countries before this has been decided in a coordinated manner".
The gradual lifting requires coordination between 30 countries, including four European Union countries who have yet to join the Schengen area - namely Bulgaria, Romania, Croatia and Southern Cyprus - and four non-EU members of the borderless zone (Norway, Lichtenstein, Switzerland, Iceland).More news: Lewis Hamilton says Bernie Ecclestone comments on race 'ignorant'
While the initial draft included 54 countries, the updated version has just 14, including Canada.
Between the lines: The guidelines allow people from countries where the average number of infections per 100,000 inhabitants over the last two weeks is similar or below the EU's, and that have reported a declining case trend.
Countries must also have a "stable or decreasing trend of new cases over this period in comparison to the previous 14 days", while the European Union will consider what measures countries are taking, such as contact tracing, and how reliable each nation's data is.
The vote is aimed at supporting the European Union travel industry and tourist destinations, particularly countries in southern Europe hardest hit by the Covid-19 pandemic.More news: Hollywood comedy legend Carl Renier has died
Earlier this week, it was reported that at least 16 U.S. states were halting plans to reopen, as reported Covid infections surged across the country. Schengen associated countries - Iceland, Lichtenstein, Norway and Switzerland - were also part of this recommendation. Four EU diplomats said they expected it to secure the required backing.
Other criteria also being considered are reciprocity and links to the EU.
The EU put in place a temporary restriction of non-essential travel to the bloc on March 17, initially for a period of 30 days but extended on several occasions.
US President Donald Trump suspended the entry of most Europeans in March.More news: Hundreds queue for COVID-19 mass testing in Beijing