Despite the outcome of the referendum, Commission President Jean-Claude Juncker has promised Ukrainian President Petro Poroshenko the Commission will put forward the eagerly awaited proposal later this month.
The news was greeted by Lithuanian MEP Petras Austrevicius, who told this website the visa issue should be separated from other events.
The ALDE deputy said, "The unfortunate Dutch referendum results should not keep Ukraine away from visa free regime with EU, as it based on delivered implementation from Ukraine."
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Further comment came from Ukraine's mission to the EU, who said that Ukraine had passed the major hurdles toward visa-free travel and now expected the EU to make its move.
The source added, "Of course, we strongly hope for this step of the Commission."
Ukraine's new ambassador to the EU was in Strasbourg to meet MEPs this week, although it is not clear if that is directly connected to the visa issue.
Elsewhere, Poroshenko said he "expects the European Commission to shortly pass a recommendation to the EU institutions regarding the granting of visa-free travels with the EU to Ukrainian citizens."
"Shortly, in a few days I expect a Commission's decision to table the legislative proposals to the EU Council and the European Parliament regarding visa-free travel. And I hope that the Ukrainians will receive it," the President said in an interview with the Ukrainian television stations broadcast on Sunday evening.
The latest development on visa liberalisation comes amid fresh turmoil in Ukraine, with Prime Minister Arseniy Yatsenyuk saying in a televised address on Sunday he is stepping down.
The prospect of visa liberalisation offers Ukrainians the most obvious benefit of closer ties with the EU.
A source at Ukraine's mission to the EU said, "Ukraine has passed the major hurdles toward visa-free travel and now expects the EU to make its move."
The move towards visa liberalisation comes partly in response to Ukraine's recent anti-corruption reforms.
However, the news will anger Eurosceptics and those in the Netherlands who last week rejected the association agreement on closer political, security and trade ties between Kyiv and the 28-nation bloc.
Less than a third of the electorate turned out in the vote but the turnout was just more than the 30 per cent required for the result to be valid.
Dutch Prime Minister Mark Rutte subsequently said that the government could not proceed with ratification of the deal which the other 27 EU countries have already approved, and which has provisionally entered into force.
Prior to the vote last week, the leader of the largest political party in the Ukraine Parliament had called on the Dutch to show a "sign of solidarity" with Ukrainian soldiers by voting 'Yes' and, on this, Austrevicius said, "The soldiers who have volunteered to fight in Ukraine are resisting Russian aggression."
Austrevicius, who is head of the European Parliament's Ukraine Friendship Group, said, "They believe in the independence of Ukraine and believe that Ukraine has a future within Europe. They are fighting for a different Ukraine, one that has been purged of its post-Soviet mentality and its corrupt politics.
"If Europe fails to understand the nature of this struggle, this will amount to a real error, a moral dereliction of duty, as it were."
Meanwhile, Yatsenyuk's announcement has triggered another political crisis in Ukraine.
The Prime Minister's announced resignation sets the stage for a new government to take over in Kyiv as soon as Tuesday.
He survived a no-confidence vote in Parliament in February, but his relationship with Poroshenko has continued to deteriorate. Volodymyr Groysman, the speaker of Parliament, is predicted to replace Yatsenyuk.
Reports indicate a new ruling coalition would consist of just two parties - the President's bloc and Yatsenyuk's People's Front - with a number of unaffiliated deputies added to reach a majority 226-vote.