The navy of Iran's Revolutionary Guard Corps said it had extended the closure to the corridor it had earlier designated for the safe passage of vessels through the waterway and declared the strait fully closed until the United States blockade on Iranian ports and ships is lifted.
In a statement late on Saturday carried by Iran's state media, the navy warned that any violating vessel would be targeted.
Shipping sources said at least two vessels reported coming under fire and being hit while trying to transit the strait.
India later said the Iranian ambassador in New Delhi had been summoned and that it had expressed deep concern to him that two Indian-flagged ships had come under fire in the strait.
State media in Iran quoted the Supreme National Security Council as saying Iranian control over the strait included demanding the payment of costs related to security, safety and environmental protection services.
State television also quoted the Supreme National Security Council as saying the US had put forward new proposals after talks mediated by Pakistan in recent days.
Iran was considering them but had not yet responded, it said.
There was no immediate sign of direct US-Iran talks taking place at the weekend, despite Trump saying on Friday that negotiations would take place.
Iran's renewed tough messaging caused new uncertainty around the conflict, raising the risk that oil and gas shipments through the strait could remain disrupted just as the US weighs whether to extend the fragile ceasefire.
Trump said the US was having "very good conversations" with Iran but that Iran wanted to close the strait again.
Iran could not blackmail the US, he said.
Trump stressed that both sides were still negotiating.
"We're talking to them, and you know, we're taking a tough stand," he said, adding that "we'll have some information by the end of the day".
Maritime security and shipping sources said some merchant vessels had received radio messages from Iran's navy saying no ships were allowed through the waterway, reversing Friday's signs that traffic might resume.
Maritime trackers had earlier shown a convoy of eight tankers transiting the narrow passage in the first major movement of ships since the US-Israeli war on Iran began seven weeks ago.
Hours earlier, Trump had cited "some pretty good news" about Iran, declining to elaborate.
But he also said fighting might resume without a peace deal by Wednesday, when the two-week ceasefire expires.
Iran had announced its temporary reopening of the Strait of Hormuz following a separate US-brokered 10-day ceasefire agreement on Thursday between Israel and Lebanon.
Israel invaded parts of southern Lebanon after the Iran-aligned Hezbollah militant group joined the fighting in early March.
But on Saturday Iran's armed forces command said transit through the strait had reverted to a state of strict Iranian military control, citing what it described as repeated US violations and acts of "piracy" under the guise of a blockade.
The spokesperson said Iran had earlier agreed, "in good faith," to the managed passage of a limited number of oil tankers and commercial vessels following negotiations but said continued US actions had forced Iran to restore tighter controls on shipping through the strategic choke point.
US Central Command said in a statement that United States forces were enforcing a maritime blockade of Iran but did not comment on the latest Iranian actions.
with DPA and AP
