* EU says referendum illegal, organisers lack legitimacy
* EU urges all sides to support May 25 presidential vote
BRUSSELS, May 11 (Reuters) - The European Union said it would not recognise the result of a referendum on self-rule held by pro-Moscow rebels in east Ukraine on Sunday, calling it illegal.
"The so-called referenda in ... parts of the Luhansk and Donetsk regions were illegal and we do not recognise the outcome. Those who organised the referenda have no democratic legitimacy," Maja Kocijancic, a spokeswoman for EU foreign policy chief Catherine Ashton, said in e-mailed comments to Reuters.
She said holding the referendum ran counter to the objectives of an agreement reached by Ukraine, Russia, the European Union and the United States last month that aimed to defuse the Ukraine crisis.
Ukraine's Crimea region was annexed by Russia in March after a similar vote.
Kocijancic said the European Union encouraged the Ukraine government to push ahead with efforts to reach out to all regions through a proposed national dialogue, including steps towards an inclusive dialogue on constitutional reform.
Ukraine's government said last week it was ready to talk to political parties and regional officials in eastern regions on ways to resolve the country's crisis, but would not talk to "terrorists".
The European Union urged all parties to support holding free and fair presidential elections on May 25, Kocijancic said.
The upheaval in Ukraine broke out after former pro-Russian President Viktor Yanukovich turned his back last year on a trade and political cooperation with the European Union in favour of a $15 billion bailout from Russia. That sparked prolonged street protests that ended with him fleeing Ukraine. (Reporting by Adrian Croft; Editing by Jon Boyle)