Senior Hamas leader Marwan Issa was killed in an Israeli air strike, the White House has said.
The deputy military commander was third in command and would be Hamas's most senior leader to die since war began on October 7.
Hamas, which controls Gaza, has not confirmed US reports of his death.
It comes after US President Joe Biden and Israeli leader Benjamin Netanyahu spoke on Monday for the first time in a month.
Mr Netanyahu agreed to send a team of Israeli officials to Washington to discuss with Biden administration officials a prospective Rafah operation as each side is looking to make "clear to the other its perspective," White House national security adviser Jake Sullivan said.
The White House has been sceptical of Mr Netanyahu's plan to carry out an operation in the southern city of Rafah, where about 1.5 million displaced Palestinians are sheltering.
National Security Advisor Jake Sullivan said Mr Biden once again urged Israel not to carry out a Rafah operation.
At the talks this week involving US Secretary of State Antony Blinken, he said officials will lay out "an alternative approach that would target key Hamas elements in Rafah and secure the Egypt-Gaza border without a major ground invasion."
"The president has rejected, and did again today, the straw man that raising questions about Rafah is the same as raising questions about defeating Hamas," Mr Sullivan said. "That's just nonsense.
“Our position is that Hamas should not be allowed a safe haven in Rafah or anywhere else, but a major ground operation there would be a mistake.
“It would lead to more innocent civilian deaths, worsen the already dire humanitarian crisis, deepen the anarchy in Gaza and further isolate Israel internationally."
The Biden-Netanyahu call also came as a new report warned that "famine is imminent" in northern Gaza, where 70% of the remaining population is experiencing catastrophic hunger.
The report warned further escalation of the war could push around half of Gaza's population to the brink of starvation.
The report came from the Integrated Food Security Phase Classification, a partnership of more than a dozen governments, UN aid and other agencies that determines the severity of food crises.
