"Last night, ten grenades exploded in several districts of Bujumbura, leaving a dozen people wounded," a senior police officer told AFP on condition of anonymity.
The officer said two soldiers were among the injured as well as civilians after the series of explosions in outlying parts of the capital.
Ban arrived in Bujumbura yesterday, hoping to bring fresh impetus to stalled efforts to resolve the 10-month-old crisis that has left more than 400 dead, caused over 240,000 to leave the country and seen violent attacks in the capital become routine.
At least four people were killed in attacks ahead of Ban's arrival Monday.
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It remains unclear who carried out the grenade blasts, which have increased in the past few weeks. Security forces, rebels and the opposition all blame each other for the killings.
"Most of the grenades exploded in deserted places, which shows that these criminals only want to show the UN secretary general that there is no security, but everything is under control," the officer said.