US President-elect Donald Trump has communicated to the Biden administration his expectation for progress toward a ceasefire between "Israel" and Hezbollah, the Israeli Ynet news website reported, as the Israeli aggression across Lebanon continues.

Citing unnamed US officials, the report indicated that US special envoy Amos Hochstein remains optimistic that the two parties will reach an agreement to end over a year of fighting and "Israel’s" ongoing ground incursion into southern Lebanon.

Ahead of the November 5 presidential election, Trump vowed to end the “suffering and destruction in Lebanon.”

He added that he wants "to see the Middle East return to real peace, a lasting peace, and we will get it done properly so it doesn’t repeat itself every 5 or 10 years."

In late October, The Times of Israel also cited two informed sources as saying that Trump has informed Israeli Prime Minister Benjamin Netanyahu that he expects "Israel" to conclude its war in Gaza by the time he assumes office.

According to a former Trump administration official and an Israeli source, the message was initially conveyed during Netanyahu’s visit to Trump’s Mar-a-Lago estate in Florida last July.

On Friday, Turkish President Recep Tayyip Erdogan expressed hope that the US President-elect would urge "Israel" to halt its war, indicating that an initial step could involve ending US arms support to the Israeli occupation regime, Reuters reported.

"Trump has made promises to end conflicts... We want that promise to be fulfilled and for Israel to be told to 'stop'," Erdogan stated to reporters aboard his flight back from Budapest, according to an official transcript.

"Mr. Trump cutting off the arms support provided to Israel could be a good start in order to stop the Israeli aggression in Palestinian and Lebanese lands," he was quoted as saying.

Read more: French FM sees Gaza, Lebanon ceasefire potential after Trump election

Palestinians won't accept US path the undermines their rights: Hamas

On its part, Hamas urged Trump to end the bias displayed by previous American administrations toward the Israeli occupation.

In a statement released on Wednesday, the Palestinian group called for genuine efforts to halt the ongoing genocide in the Gaza Strip, the West Bank, and Lebanon, emphasizing the need for a shift in US foreign policy to address the suffering in the region and live up to the expectations of American citizens calling for a ceasefire. 

"Our position toward the new US administration depends on its stance and [actions] toward the Palestinian people and their just cause," the movement stated.

Hamas emphasized that it "will not accept any path that undermines the freedom of the Palestinian people, their right to self-determination, and the establishment of their independent state with al-Quds as its capital."

It stressed that the Trump administration "must realize that our people are determined to confront the occupation and will not accept any path that infringes upon their legitimate rights."

Hamas pointed out that all successive US administrations since the occupation of Palestine have taken negative positions on the Palestinian cause and that the previous US administration aligned with the Israeli occupation's genocidal war, providing the government with both political and military cover. 

Read more: Will Trump’s 2nd term bring change to the US' Middle East strategy?