Mr Trump cited footage that Washington says shows Iranian forces in a small boat taking an unexploded mine off the hull of one of the ships.
UN Secretary General Antonio Guterres said the truth needed to be "clearly established".
Russia has warned against drawing "hasty conclusions".
The blasts came a month after four oil tankers were damaged in an attack off the coast of the United Arab Emirates. The US blamed Iran for that attack, but did not produce evidence. Iran also denied those accusations.
Tensions between the US and Iran have escalated significantly since US President Donald Trump took ...
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