Images, verified by Reuters as having been filmed from the shore of the port of Basra, showed the ships engulfed in massive orange fireballs that lit up the night sky.
Iraqi authorities said the vessels had been attacked overnight by Iranian boats laden with explosives. 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, which was launched by the United States and Israel and has so far killed about 2000 people, has caused the biggest disruption to global energy supplies since the oil shocks of the 1970s.
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 UAE, Bahrain and Oman.
Oil prices that had come down earlier in the week after Trump said the war would soon be over blasted back above $US100 a barrel.
Iran has said it would not allow oil through the world's most important energy trade route - the Strait of Hormuz that runs along its coast - until US and Israeli attacks ceased, and it would not conduct any negotiations with Washington.
Citibank announced on Thursday it would temporarily shut its branches in the UAE, a day after Iran said it considered banks to be legitimate targets and warned Middle East residents to stay 1000 metres from them.
HSBC has shut branches in Qatar.
Thursday's surge in oil prices came despite the announcement the previous day that developed countries would release a record 400 million barrels of oil from their strategic reserves, nearly half from the United States.
Trump, whose Republican Party is trying to hold on to Congress in an election in November, has repeatedly tried to calm energy markets this week by saying the war will soon be over and the surge in oil prices will be short-lived.
But he has not fully explained how the war will end, or presented a plan to reopen the blockaded strait.
US and Israeli officials say the aim is to destroy Iran's missile and nuclear programs, but Trump has also demanded Iran's "unconditional surrender" and the power to determine its leaders.
"You never like to say too early you won. We won," Trump told a campaign-style rally in Kentucky on Wednesday, adding, "In the first hour it was over."
The United States had "virtually destroyed Iran", he said.
But he said: "We don't want to leave early do we? We got to finish the job."
But three sources familiar with the matter told Reuters that US intelligence indicated that Iran's leadership was still largely intact and not at risk of collapse any time soon.
Iran has made clear that its strategy now is to impose a prolonged economic shock on the world to force Trump to back off.
The spokesperson for Iran's military command said the world should prepare for oil prices of $US200 a barrel because of instability caused by the US.
Trump said Wednesday's announcement of the huge release of reserves would "substantially reduce oil prices as we end this threat to America and the world".
Iran also hit fuel tanks in Bahrain, and drones struck oil storage facilities at Oman's Salalah port on Wednesday.
Saudi Arabia said it had also intercepted several drones heading towards its Shaybah oilfield on Thursday.
