The Lebanese embassy in the US said it had "received confirmation of Hezbollah's acceptance of the US proposal for a mutual cessation of attacks".
Israeli Prime Minister Benjamin Netanyahu confirmed the agreement, but warned strikes on Beirut would go ahead "if Hezbollah does not stop attacking our cities and civilians".
The statements came after US President Donald Trump said he had spoken to both Netanyahu and Hezbollah representatives and "they agreed that all shooting will stop", after Iran warned that Israeli military actions in Lebanon were a threat to the current US-Iran ceasefire.
In a statement late on Monday, the Lebanese embassy said that "under the proposed arrangement, Israeli strikes on Beirut's southern suburbs would cease in exchange for Hezbollah refraining from attacks against Israel". It added that the ceasefire was "to be extended to encompass all Lebanese territory".
However Netanyahu said: "At the same time, the IDF [Israel Defense Forces] will continue to operate in southern Lebanon as planned."
After Trump said both sides had agreed to stop fighting some clashes continued.
Hezbollah said it had launched three attacks at Israeli tanks and soldiers near two villages in northern Israel, using drones and "a barrage of artillery shells".
