Didier Trebucq said nearby islands including Barbados, Antigua and Barbuda could also be badly affected.
He said the UN was setting up an international funding appeal.
About 20,000 people have been evacuated from their homes since La Soufrière volcano began erupting last Friday.
It had not previously erupted since 1979.
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St Vincent volcano: UN warns humanitarian crisis will last months
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"We are expecting that continuous explosions and ash fall will continue over the coming weeks in Saint Vincent and the Grenadines, but also in neighbouring islands such as Barbados, which has also been severely affected... as well as Saint Lucia and Grenada," he told reporters.
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