In Iran, one politician responded by renewing a threat to blockade the Strait of Hormuz, an oil export route vital to the global economy, and another said Tehran should cut off crude shipments to the EU immediately.
That might hurt Greece, Italy and other ailing economies which depend heavily on Iranian oil and, as a result, won as part of the EU agreement a grace period until July 1 before the embargo takes full effect.
A day after a US aircraft carrier, accompanied by a flotilla that included French and British warships, made a symbolically loaded voyage into the Gulf in defiance of Iranian hostility, the widely expected EU sanctions move is likely to set off yet more bellicose rhetoric in an already tense region.
Some analysts say Iran, which denies accusations that it is seeking nuclear weapons, could be in a position to make them next year.
So, with Israel warning it could use force to prevent that happening, the row over Tehran’s plans is an increasingly pressing challenge for world leaders, not least US President Barack Obama as he campaigns for re-election in November.