WASHINGTON, June 1 (Xinhua) -- U.S. President Donald Trump said Monday that the U.S.-Iran talks "are continuing, at a rapid pace," following his announcement that Israel and Hezbollah have agreed to halt fire.

Trump's remarks came hours after Tehran said it was suspending its exchange of messages with Washington through mediators in protest of Israel's military operations in Lebanon.

"Talks are continuing, at a rapid pace, with the Islamic Republic of Iran," Trump wrote on Truth Social.

In an earlier post on Monday, Trump said he had spoken by phone with Israeli Prime Minister Benjamin Netanyahu and with representatives who conveyed messages from Hezbollah, claiming that both sides had agreed to halt hostilities.

Israel would not send troops to Beirut, Lebanon's capital, Trump added, describing his call with Netanyahu as "very productive."

On Sunday, Israel claimed that its forces had captured southern Lebanon's Beaufort Ridge, including the strategic castle at its summit -- an area located beyond the "security zone" Israel has maintained since the ceasefire with Lebanon.

The move, which media reports called Israel's "deepest advance into Lebanon" in over 20 years, drew condemnation from across the Arab world as well as from France, Germany, and the United Kingdom.