US President Joe Biden reportedly asked Israeli Prime Minister Benjamin Netanyahu in a call on Wednesday to move troops back from Gaza's border with Egypt as part of an initial phase of a ceasefire deal so that talks could continue.
Netanyahu has insisted Israeli forces remain in the Philadelphi corridor (also known as the Salah al-Din corridor) border strip, a stance that could prevent an agreement from being reached.
However following Biden's call, he agreed to give up an Israeli troop position along the Egypt-Gaza border, three Israeli officials told US news website Axios.
The move led to Washington backing Israel's stance that other troops stay in the Philadelphi corridor in the initial stage of an agreement, according to an Israeli official.
Egypt then "had to agree" to pass to Hamas maps containing the new positioning of Israeli troops, Axios said, citing the same official.
Israeli officials did not expect Hamas to accept the altered maps with a small decrease in the Israeli deployment.
Netanyahu accepted shifting one Israeli position by just a few hundred metres "in a way that does not harm operational control" along the strategic border strip, according to an aide.
"The [army] is deployed all along the Philadelphi corridor. The prime minister stands by the principle that this situation will continue," the aide said.
A US National Security Council spokesperson declined to comment.
"We do not comment on diplomatic discussions and those doing so second-hand jeopardise efforts to conclude an agreement and bring the hostages home," the spokesperson was quoted as saying by Axios.
"On all issues, our position is clear and firm that the terms of the deal must be implemented in full. Nothing more and nothing less."
Israel's war on Gaza, which began more than 10 months ago, has killed at least 40,334 people and injured 93,356, according to the Palestinian enclave's health ministry.
Hospitals, ambulances, and residential buildings have been attacked and South Africa has accused Israel of committing genocide in Gaza at the International Court of Justice, the United Nations' top tribunal.
Reuters contributed to this report.