"The SBU was able to prevent a series of 15 acts of terror [planned] for the eve and during the Euro soccer championship,” the agency's chief, Vasily Gritsak, told reporters.
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The SBU said the suspect — a 25-year-old French citizen — was detained with rocket-propelled grenade launchers, 275 pounds of TNT, five Kalashnikov machine guns, 100 electric detonators and 20 balaclavas.
"The Frenchman spoke negatively about his government's actions, mass immigration, the spread of Islam and globalization, and also talked about plans to carry out several terrorist attacks," according to Gritsak.
Authorities across Europe are on high alert after Islamist militants killed 130 people in Paris last November and suicide bombers killed 32 people at Belgium's main international airport and on the Brussels metro in March.
The SBU did not name the suspect.
The Paris police prefect, Michel Cadot, declined to comment on the information from Ukraine, saying only that "there is no specific threat against any site in the Euro."
The Paris prosecutor's office, which handles terrorism cases at a national level, said no investigation had yet been opened.
Gritsak said the SBU has been monitoring the suspect for months and sold him deactivated weapons after they found out that he was looking to purchase the arms. He was detained at the Polish border last month as he tried to return with the cache, according to the SBU, which also tweeted pictures of the arrest.
Ukrainian troops and Russia-backed separatists have fought in the east since April 2014, killing nearly 9,400 people. It was not immediately clear which side of the conflict the French suspect had contacts with.
France is deploying 90,000 security forces for Euro 2016 and French President Francois Hollande said Sunday night that the threat of attacks won't stop it from being successful.
Alexey Eremenko is a producer in NBC News’ Moscow bureau. He previously worked at Russia's sole English-language daily The Moscow Times and on the English desk of the RIA Novosti newswire. His main beats included politics, space and environment, and he has reported from Afghanistan, Mali, Iran and across Russia.
Alastair Jamieson is a London-based reporter, editor and homepage producer for NBC News.