The EU-Ukraine association agreement cannot be signed until certain conditions are met by the Ukraine, namely on the supremacy of law, the Commission has said.
Speaking on behalf of the EU's foreign affairs representative, Stefan Fule said the Ukraine must redress the "systemic problem" of "selective justice", conduct free and fair elections and resume delayed reforms before it can become a closer EU ally.
The association agreement is aimed at establishing political association and economic integration between the European Union and Ukraine.
The parliament's social democrat and centre-right groups said they wanted to see the agreement ratified, but only if the Ukraine delivers the desired changes.
MEPs used the debate to condemn the treatment of jailed opposition leader treatment Yulia Tymoshenko, who went on hunger strike in April after accusing prison staff of beating her during an attempt to move her to hospital.
Ukraine denies her allegations, including her claim that she is being punished as an act of political revenge by President Viktor Yanukovych.
Mr Fule said to MEPs: "We have told the Ukrainian authorities that providing Yulia Tymoshenko with adequate treatment in Ukraine or outside it will be the first step towards a restoration of trust."
Ms Tymoshenko was jailed for seven years in October 2011 for abuse of office during her time as prime minister. Her trial has been delayed again until late June.
Several high profile leaders, including Commission President Jose Manuel Barroso, have said they will not go to the European football championships in Ukraine - a decision which divided MEPs.
Dutch Liberal Johannes Cornelis Van Baalen said Euro 2012 should be used to draw attention to the human rights situation there, and help the country to make progress in this area.
And Polish euro-sceptic Zbigniew Ziobro questioned whether the boycott would improve standards in Ukraine.
However, Green group leader Rebecca Harms argued in favour of a political boycott of the Ukraine, in protest at the "systematic persecution" of high-ranking opposition politicians.
She said the EU was making headway in attracting attention to the situation there, but that "we cannot rest on our laurels", she told MEPs.
Wrapping up the debate, Mr Fule said EU leaders who had stated their intention not to attend Euro 2012 were refusing to go in a personal rather than professional capacity, and it therefore did not amount to a "boycott".
"We hope Euro 2012 will be a great success," he added.
Ms Tymoshenko's daughter was present in the European Parliament during the debate.
MEPs passed a resolution on the latest developments in Ukraine, on
24 May 2012.