Iran has made a ceasefire in Lebanon a condition for any peace deal with the United States, and has suggested in recent days that it could intervene directly in support of Hezbollah if Israel keeps up or escalates attacks there.
Lebanese President Joseph Aoun said the ceasefire would come into force within 24 hours of all concerned parties approving it.
However, Hezbollah leader Naim Qassem rejected the Washington DC declaration, insisting "resistance will continue".
There was no immediate response from Israel, Lebanon or the US to Qassem's remarks.
Hezbollah is not a party to the US-brokered agreement reached between Israel and the Lebanese government on Wednesday but would be required to halt attacks.
Under the agreement announced in the US on Wednesday, Hezbollah militants would be disarmed.
Israel kept up strikes in southern Lebanon on Thursday and Defence Minister Israel Katz said Israeli forces would not be withdrawing from the area or halting operations in the country, which they invaded in March in parallel with the war in Iran.
The commander of Iran's Revolutionary Guards Quds Force - which established Hezbollah in 1982 - said "the minimum demand of the resistance" was Israel's withdrawal to positions it held before the war began.
"Our initial condition for accepting a ceasefire in the regional war was a ceasefire on all fronts, including Lebanon," a separate statement from the Guards said.
Israel must stop its attacks in Lebanon, leave areas it occupies and retreat behind international borders, said the statement, carried by state media on Thursday.
Hostilities between Hezbollah and Israel reignited on March 2, when the group opened fire in support of Iran as it came under US and Israeli attack.
The war has continued despite several ceasefires declared from the US since April.
Last week, Iran and the US signalled progress towards a tentative initial agreement to halt the war and reopen the Hormuz Strait, but the two sides have yet to sign off on the deal, which would leave more complex negotiations for later.
Iran's Supreme Leader Ayatollah Mojtaba Khamenei said on Thursday that Iran's enemies had already been defeated on the battlefield and were now seeking to sow internal divisions.
Khamenei has not been seen in public since he succeeded his father, who was killed in an air strike at the start of the war.
In addition to Iran conditioning a deal on an end to fighting in Lebanon, it also wants access to billions of dollars in oil revenue, waivers on sanctions on crude exports, a lifting of a US blockade on its ports and leverage over the strait.
Trump has said his top priority is to stop Iran from acquiring nuclear weapons.
Iran says its atomic program is for peaceful purposes.
The United Nations nuclear watchdog sent a report to member states on Thursday repeating its calls on Iran to urgently inform the agency of the fate of its enriched uranium since its atomic sites were bombed a year ago and let inspections resume fully.
Iran only granted the International Atomic Energy Agency's inspectors access to a single nuclear facility in recent months, IAEA chief Rafael Grossi notes in the report.
It was "critical" for the nuclear watchdog "to conduct verification activities in Iran without delay," Grossi said, despite acknowledging that the US-Israeli strikes on Iran's nuclear sites "have created an unprecedented situation".
Iran has largely suspended its co-operation with IAEA inspectors since the US and Israel began attacking Iran on February 28.
with DPA
