US President Donald Trump said on Monday that talks between Washington and Tehran "are continuing, at a rapid pace," after Iran signaled a suspension of indirect contact with the United States amid Israel's escalating military operations in Lebanon.

Hours earlier, Iran's semi-official Tasnim news agency reported that Tehran had halted the exchange of messages with Washington through mediators in protest at Israel's actions in Lebanon.

"There will be no dialogue" until Iran's demand for an immediate cessation of Israeli military operations in Gaza and Lebanon is met, Tasnim quoted sources as saying.

The report added that Iran and its allies had placed on the agenda plans to "completely block the Strait of Hormuz and activate other fronts, including the Bab el-Mandeb Strait," in response to the developments.

The remarks came as Israel stepped up military operations in Lebanon. Israeli Prime Minister Benjamin Netanyahu and Defense Minister Israel Katz said on Monday they had ordered air strikes on Beirut's southern suburb of Dahieh, accusing Hezbollah of repeatedly violating the ceasefire agreement.

Iran's Khatam al-Anbiya Central Headquarters warned Israel against targeting Beirut, according to the official IRNA news agency. In a statement, the command warned residents in northern Israel and military settlements in the occupied Palestinian territories to evacuate if Israeli attacks on Beirut continue.

Trump says Israel will not send troops into Beirut

Earlier on Monday, Trump said he had spoken by phone with Netanyahu and had received messages from Hezbollah through intermediaries, claiming that both sides had agreed to halt hostilities.

Israel would not send troops into Beirut, Trump said, describing his conversation with Netanyahu as "very productive."

Lebanese authorities confirmed that Hezbollah has agreed to a US proposal for a "mutual cessation of attacks" with Israel, according to a statement by the Lebanese presidency on Monday, citing the Lebanese embassy in Washington.

Netanyahu, however, later reiterated that Israel's position remained unchanged and that the Israeli military would continue its planned operations in southern Lebanon.

On Sunday, Israel said its forces had captured the Beaufort Ridge in southern Lebanon, including the strategic Beaufort Castle at its summit, an area located beyond the "security zone" Israel has maintained since the ceasefire with Lebanon.

The move, described by media reports as Israel's deepest advance into Lebanon in more than two decades, drew condemnation from Arab countries as well as France, Germany and Britain.

(With input from Xinhua)