The Lebanon conflict spiralled out of the US-Israeli war with Iran, with the Iran-backed Hezbollah opening fire in support of Tehran on March 2, prompting an Israeli offensive in Lebanon just 15 months after the previous major conflict.
The Israeli security cabinet convened late on Wednesday to discuss a possible ceasefire in Lebanon.
"Peace in Lebanon is essential for (Iran) peace talks," Pakistan's foreign ministry said on Thursday.
In a post on Truth Social, Trump said he was "trying to get a little breathing room" between Israel and Lebanon.
"It has been a long time since the two leaders have spoken, like 34 years. It will happen tomorrow. Nice!" Trump wrote.
The post did not give any further details.
Gila Gamliel, a member of Israel's security cabinet, told Israel's Army Radio that Prime Minister Benjamin Netanyahu would "speak for the first time with the president of Lebanon after so many years of no contact between the two countries".
A senior Lebanese official told Reuters Lebanon had no information about a call between Lebanese President Joseph Aoun and Netanyahu.
The Lebanese government has been sharply at odds with Hezbollah over its decision to enter the war, having spent the past year seeking to secure the peaceful disarmament of the group founded by Iran's Revolutionary Guards in 1982.
Washington on Wednesday expressed optimism about reaching a deal to end the war with Iran.
The sides agreed a two-week ceasefire in the Iran war on April 8, following mediation by Pakistan.
Israel and the US have said the campaign against Hezbollah was not part of that ceasefire, though Pakistan's prime minister had said the truce would include Lebanon, as demanded by Iran.
A senior Israeli official and a senior Lebanese official said on Wednesday Netanyahu's government was under heavy pressure from Washington to reach a ceasefire in Lebanon.
Netanyahu said the Israeli military continued to strike at Hezbollah and was about to "overcome" the southern Lebanese border town of Bint Jbeil.
The senior Lebanese official said Lebanon's assessment was that Israel wanted to secure a victory in Bint Jbeil before diplomatic progress could be made.
Israeli and Lebanese ambassadors held rare talks in Washington on Tuesday.
Iran has said Lebanon must be included in any agreement to end the wider war in the Middle East, while Washington has pushed back, saying there is no link between the two sets of talks.
Hezbollah on Wednesday condemned Tuesday's meeting in Washington, saying it would deepen the rift among Lebanese.
