In the defiant address, Khamenei said the United States must close all its bases in the region.
The strait, which runs past Iran's coast and supplies a fifth of the world's oil, should remain shut to put pressure on the enemy, he said.
Iranian state television offered no explanation of why Khamenei, 56, did not appear on camera.
Israeli intelligence assessments suggest he was wounded in the war, likely in the February 28 Israeli strike that killed his father, the 86-year-old late Supreme Leader Ayatollah Ali Khamenei.
Two tankers were ablaze in an Iraqi port on Thursday after a hit by suspected Iranian explosive-laden boats, a step-up in attacks that have cut off oil from the Middle East.
Images verified by Reuters as having been filmed from the shore of the port of Basra showed ships engulfed in massive orange fireballs that lit up the night sky, after the attacks, which Iraqi authorities blamed on Iranian boats.
At least one crew member was killed.
Hours earlier, three other ships had been struck in the Gulf.
Iran's Revolutionary Guards claimed responsibility for at least one of those attacks, on a Thai bulk carrier that was set ablaze, which the Guards said had disobeyed their orders.
Another container vessel reported being struck by an unknown projectile near the United Arab Emirates on Thursday.
The war that began with a US-Israeli bombing campaign at the end of February has so far killed about 2000 people and caused what the International Energy Agency describes as the biggest disruption to global energy supplies in history.
Undermining US and Israeli claims to have knocked out much of Iran's stock of long-range weapons, more drones were reported on Thursday flying into Kuwait, Iraq, the United Arab Emirates, Bahrain and Oman.
Lebanon's Iran-backed militia Hezbollah fired its biggest volley of rockets into Israel of the war, prompting fresh Israeli strikes on Beirut.
Oil prices soared back above $US100 a barrel, having come down earlier in the week when US President Donald Trump said the war would be over soon.
Iranian authorities have said they will not let oil through the Strait of Hormuz, the world's most important energy trade route, until US and Israeli attacks cease.
with AP
