Israel-Gaza updates: 22, including 18 children, reported dead in Rafah strikes

Secretary of State Antony Blinken spoke with Israeli war cabinet minister Benny Gantz, during which Blinken "continue[d] to send the same messages in all his conversations -- which is we do not want to see further escalation of the conflict," according to spokesperson Matt Miller.

Miller declined to say whether the U.S. assessed the threat of escalation had fallen, but an administration official said the amount of time that has already elapsed since Iran’s weekend attack had boosted hopes that Israel would exercise constraint.

Miller batted down reports that Iran and the U.S. were communicating through intermediaries in the wake of Tehran’s attack on Israel.

"There have not been such messages delivered. It's been days since we've communicated -- since we've sent messages to the government of Iran," Miller said. "And I say that as a reminder of something we've said before: Oftentimes, the Iranian government has misled the world about either messages they've passed to us or messages that we have passed to them."

-ABC News’ Shannon Crawford

U.K. Prime Minister Rishi Sunak spoke on the phone with Israeli Prime Minister Benjamin Netanyahu on Tuesday. While Netanyahu thanked Sunak for the U.K.'s support to counter Iran's weekend attack on Israel, Sunak also had harsh words for Netanyahu about the deepening humanitarian crisis in Gaza.

"On Gaza, the Prime Minister said he remained gravely concerned about the deepening humanitarian crisis," a Downing Street spokesperson said. "The U.K. wanted to see a massive step change in aid access to flood Gaza with vital supplies, including Israel opening up new aid routes as quickly as possible. The Prime Minister said it was deeply disappointing that Hamas blocked a deal at the weekend that would have saved Palestinian lives and secured the safe release of hostages."

Prime Minister Benjamin Netanyahu's war cabinet met for the third day in a row on Tuesday to consider an Israeli response to Iran's weekend attack.

But Tuesday’s meeting ended with no final decision made about an Israeli response, according to an Israeli source with knowledge of the meeting. A variety of options are still being considered, the source said.

Iranian Foreign Minister Hossein Amir-Abdollahian told Chinese Foreign Minister Wang Yi on a call that "Iran is willing to exercise restraint and has no intention of further escalating the situation," according to the Chinese foreign ministry’s readout of the conversation.