"The security situation around the tournament, and in particular in Ukraine following the recent events in Dnipropetrovsk, was thoroughly reviewed," UEFA said in a statement on Monday following a meeting with members of the local organising committee.
"UEFA received a clear assurance by the governments of the host countries that all necessary steps are being taken to guarantee the safety of all visitors, from fans to participating players."
Ukraine is co-hosting the event with Poland.
Thirty people were injured on Friday when four bombs planted in rubbish bins in various downtown locations of Dnipropetrovsk exploded at short intervals in the city of 1.3 million in what prosecutors said was an "act of terrorism".
UEFA also briefly referred to the political situation in Ukraine where relations with the European Union have been strained by the conviction of leading opposition politician Yulia Tymoshenko last October.
"UEFA alerted the Ukrainian delegation about the concerns raised by the political situation in Ukraine among European politicians and media," said UEFA.
"Even though UEFA, as a sports organisation, never interferes in political matters, UEFA has asked the Ukrainian delegation to convey these concerns to the competent authorities."
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