The warring sides each accused the other of violating the agreement reached two weeks ago to end the four-month-old conflict.
Washington said it hit Iranian targets overnight. Iran said it responded on Saturday by striking targets linked to US forces.
Saturday's attack on a tanker in the strait followed another on a cargo ship on Thursday that triggered the latest escalation. Iran has made a fresh bid to assert control over the world's most important energy shipping route, which has begun to reopen after months of disruption.
Britain's UKMTO maritime security agency said the tanker hit on Saturday had sustained damage to its bridge, with all crew reported safe. The Joint Maritime Information Center, run by a coalition of navies protecting shipping, raised its security threat level as a result of recent incidents.
But Iranian state television reported the Revolutionary Guards fired "warning shots" towards unspecified vessels attempting to pass through channels not approved by Iran, and that was prompting other ships to seek Iranian permits before attempting to cross the strait.
Earlier, Iran's foreign ministry said it launched "defensive" attacks on US-linked military targets, while Bahrain, which hosts the US Navy's regional headquarters, reported an Iranian drone attack.
Iran has accused the US of failing to uphold the interim agreement, in particular by failing to sustain a promised ceasefire in Lebanon, which US ally Israel invaded in March in pursuit of the Iran-backed militant group Hezbollah.
Israel insists it will not withdraw from territory it has seized and Hezbollah has repeatedly rejecting calls to give up its arms as long as Israeli troops remain in place.
Lebanese state television reported an Israeli drone strike on Saturday in the Nabatiyeh area in the south.
The Israeli military said it had targeted a person who posed a threat to its forces. Hezbollah leader Naim Qassem rejected the day-old Israel-Lebanon agreement as surrender, and said it was "null and void".
Israeli Defence Minister Israel Katz praised the agreement, saying it allows Israel to maintain its occupation of a so-called security zone in Lebanon and bars the return of displaced residents.
Mohsen Rezaei, an adviser to Iran's supreme leader, said Washington had violated the war-ending memorandum of understanding by supporting what he called proxy forces in the region and creating tensions in the Strait of Hormuz.
Throughout the war, Iran has responded to US attacks by hitting neighbouring Gulf states that host large US military bases.
Iranian state television said the Revolutionary Guards had delivered "a decisive response" after US forces hit a communications tower in the port city of Sirik. Iran's Mehr news agency said the Iranian port was operating normally with no damage reported to facilities or equipment.
Bahrain said Iran's latest attacks violated the memorandum of understanding.
Hundreds of ships, including tankers laden with oil, have been blockaded inside the Gulf since war broke out.
As they began leaving through the strait over the past two weeks, oil prices have tumbled close to pre-war levels on the resulting surge in supply.
Washington has been promoting a southern lane along the coast of Oman, while Tehran, which ultimately aims to charge fees for use of the strait, wants ships to use a northern route through its waters and under its control.
Ebrahim Azizi, head of the Iranian parliament's national security committee, said any violation of Iran's shipping instructions would be met decisively.
US Vice President JD Vance said the Americans had adhered to the ceasefire deal and blamed Iran for any return to conflict that might result from its actions.
"Iran signed a ceasefire agreement. We have honored it. If they have disagreements about how the MOU is being applied, they can pick up the phone. But violence will be met with violence," Vance said on X.
The escalation unfolded over the weekend while markets were closed, giving the sides two days to stake out tough positions and exchange fire without causing any immediate oil price impact.
Over the last two weekends, bitter words on Friday and Saturday were followed by more ameliorative positions from both sides in time for markets to reopen on Monday.
