Each of the warring sides has accused the other of violating the agreement reached two weeks ago to end the four-month-old conflict.
"There may come a point when we are no longer able to be reasonable, and will be forced to militarily complete the job that we very successfully started. If that happens, the Islamic Republic of Iran will no longer exist!" US President Donald Trump posted on social media on Saturday.
US Central Command said its forces carried out fresh strikes after a Panama-flagged tanker was attacked by an Iranian drone early on Saturday. In Iran, state broadcaster IRIB said early on Sunday that explosions were heard in Sirik in southern Iran, without providing further details.
"Iran was given a chance to honor the ceasefire agreement but elected not to," US Central Command said in a statement.
The strikes were "in direct response to continued Iranian aggression against commercial shipping" and targeted Iranian military surveillance, communications, air defence, drone storage and mine-laying facilities. it said.
Washington said earlier that 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.
Iranian state television reported that the Revolutionary Guards had fired "warning shots" toward unspecified vessels attempting to pass through channels not approved by Iran, and that this was now 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 not upholding the interim agreement, in particular by not sustaining a promised ceasefire in Lebanon, which Israel invaded in March in pursuit of the Iran-backed militant group Hezbollah.
Israel and Lebanon have repeatedly agreed to US-brokered ceasefires, the latest of which was announced on Friday. But these have had only limited overall impact, with Israel insisting it won't withdraw from territory it has seized and Hezbollah repeatedly rejecting calls to give up its arms as long as Israeli troops remain.
Lebanese state television reported an Israeli drone strike on Saturday in the Nabatiyeh area in the south, which has experienced Israeli strikes throughout the conflict. 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 a surrender, and said it was "null and void".
With hundreds of thousands of Lebanese, mainly Shi'ite Muslims, still unable to return to homes in Israeli-occupied areas, anger over the agreement has spread beyond Hezbollah to the wider Shi'ite community.
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.
Iran has also struck 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 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.
