Representative Nancy Pelosi, a former House speaker and a key ally of Joe Biden, signed a letter on Friday from dozens of congressional Democrats to the president and Secretary of State Antony Blinken, urging a halt to weapons transfers to Israel.
Israel's military assault on Gaza has come under increasing international criticism as the Gaza health ministry has reported more than 33,000 people have died in the war and the narrow coastal enclave suffers widespread hunger.
Support from Pelosi, a veteran member of Biden's Democratic Party, for stopping the transfer of weapons to Israel showed that the view is increasingly becoming mainstream in the party.
Meanwhile, Hamas said that Israel's proposal that it received from Qatari and Egyptian mediators did not meet any of the demands of Palestinian factions.
However, the group added in a statement that it would study the proposal, which it described as "intransigent," and deliver its response to the mediators.
A Hamas official told Reuters on Monday that the group has rejected the Israeli ceasefire proposal made at talks in Cairo, and Israeli Prime Minister Benjamin Netanyahu said a date was set for an invasion of Rafah, Gaza's last refuge for displaced Palestinians.
Israel and Hamas sent teams to Egypt on Sunday for talks that included Qatari and Egyptian mediators as well as CIA Director William Burns.