The comments came amid continued fears of escalations between Israel and Hezbollah in Lebanon.
According to Channel 13, a message was sent to Israel informing them that tensions with Hezbollah and Iran need to be reduced at some stage as “the [US] aircraft carriers will not be able to stay in the area forever”.
Fears of a full-scale war surged following Israel’s assassination of Hezbollah commander Fuad Shukr, and the killing of Hamas leader Ismail Hanniyeh in Iran last July.
Hezbollah retaliated against the assassination by launching a large-scale missile and drone attack on targets in northern Israel on 25 August, however, further retaliations are expected.
Following the missile and drone attack, the US Department of Defence extended the deployment of two US aircraft carrier strike groups.
US Secretary of Defence Lloyd Austin reiterated Washington’s commitment to supporting Israel against any threats from Iran and Hezbollah following the the Lebanese group’s attack.
The aircraft carrier Theodore Roosevelt had arrived in the region in early July and the Abraham Lincoln carrier arrived in mid-August.
According to reports, Austin recently called Israeli defence minister Yoav Gallant, with the two defence chiefs reportedly discussing the situation along the borders with Lebanon.
Iran has so far not retaliated for the assassination of Haniyeh, while ceasefire talks continue to stall.
US Secretary of State Antony Blinken said on Thursday it was incumbent on both Israel and Hamas to say “yes” on remaining issues to reach a Gaza ceasefire deal, which has faced obstacles in negotiations for months.
“Based on what I have seen, 90 percent is agreed but there are a few critical issues that remain”, including the -called Philadelphi corridor which separates Egypt and Gaza, Blinken stated at a press briefing in Haiti.
Israeli Prime Minister Benjamin Netanyahu has insisted on keeping troops on the corridor, while Hamas has demanded the withdrawal of all Israeli troops from Gaza.
Blinken noted there were also some gaps in the agreement in how Israeli and Palestinian captives are exchanged.
“I expect in the coming days, we will share with Israel, and they (Qatar and Egypt) will share with Hamas our thoughts, the three of us, on exactly how to resolve remaining outstanding questions,” he added, referring to the US and mediators Qatar and Egypt.
Since the start of the war on Gaza, Israel has killed almost 40,900 Palestinians and wounded around 94,500 others in the same time frame. Around 10,000 others are believed to be trapped under the rubble.
The war on the besieged enclave has plunged it into a deep humanitarian crisis and levelled entire neighbourhoods, also destroying essential infrastructure and medical facilities.