The EU warned Burundi on Monday it might impose sanctions on those responsible for violence and consider other steps against the aid-reliant nation, plunged into turmoil by the president's plan to run for a third term.
A grenade attack killed four people on Sunday. President Pierre Nkurunziza's opponents say his bid for another five years in office is unconstitutional, while he cites a court ruling that found he could run.
It is the worst political crisis since Burundi emerged from ethnically-fueled civil war in 2005. The unrest has worried a region with a history of ethnic conflict, particularly next door Rwanda, where there was a genocide in 1994.
"The EU is determined to adopt, if necessary, targeted restrictive measures against those whose actions might have led or might lead to acts of violence and repression and serious human rights violations," EU foreign ministers meeting in Luxembourg said in a statement.
The European Union funds about half the annual budget of Burundi, one of the world's poorest nations, and diplomats have said in the past donors would seek targeted sanctions rather than broad steps that could harm the population.
But EU ministers warned that the situation could push them to consider reviewing broader relations between Burundi and the EU, comments suggesting some aid could be suspended.
The EU, Belgium and the Netherlands have already cut some aid flows, mainly related to supporting the elections.
EU demands, echoing those of African states, include ensuring the media operates freely to ensure a fair vote after several independent radio stations were shut.
But ministers said there was a "strong likelihood" that this would not be possible in the election timeframe.
Both the parliamentary poll due on June 29 and presidential vote on July 15 have been delayed by several weeks because of protests, in which stone-throwing demonstrators have clashed with police who have shot at them.
Police said four people were killed and 27 wounded on Sunday in a grenade attack on a bar in Ngozi, near the president's home village, and a blast in the northern town of Kirundo wounded one person.
Another grenade attack on a police station in Bujumbura's Musaga district wounded a police officer. A series of similar grenade blasts on Friday injured 11 police.
A rights group said last week the death toll since protests erupted in late April was at least 70. The president's ruling CNDD-FDD party put it at more than 40.