"Armenia and Turkey should use the centenary of the Armenian genocide to renew diplomatic relations, open the border and pave the way for economic integration," a statement by the EU legislature said on Wednesday after it adopted a non-binding resolution on the issue.
The Members of the European Parliament (MEP) also called on Turkey to open its archives and "come to terms with its past".
The EU institution praised Turkish President Recep Tayyip Erdogan and other officials for "offering condolences and recognizing atrocities against the Ottoman Armenians", Al Jazeera reported.
Ankara agrees that many Armenians died in ethnic fighting and the deportation process between 1915 and 1917, during World War I, putting its estimate at 300,000 causalities.
Armenia says 1.5 million died in the whole process, including the march to Syria, in what they say was genocide. Turkey says there was no systematic attempt to destroy Armenians.
The centenary of the 1915 killings is to be commemorated on April 24.
MEPs invited Armenia and Turkey to use examples of successful reconciliation between European nations by ratifying and implementing, without preconditions, the protocols on the establishment of diplomatic relations, opening the border and actively improving their relations.
In a statement made right after the resolution was passed, the Turkish foreign ministry said that the resolution was "inconsistent with international law" and it "exceeded the institution's jurisdiction".
"We don't take seriously this resolution that slaughters history and law," the statement said.
"Through the resolution it passed, the European Parliament has repeated the mistake it made in the past," it added.
The European Parliament described the killings as a "genocide" in 1987.