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The United States intends to launch further strikes at Iran-backed groups in the Middle East, the White House national security adviser said on Sunday, after hitting Tehran-aligned factions in Iraq, Syria and Yemen over the last two days.

The United States and Britain unleashed attacks against 36 Houthi targets in Yemen, a day after the US military hit Tehran-backed groups in Iraq and Syria in retaliation for a deadly attack on US troops in Jordan.

"We intend to take additional strikes, and additional action, to continue to send a clear message that the United States will respond when our forces are attacked, when our people are killed," White House National Security Adviser Jake Sullivan NBC’s Meet the Press programme on Sunday.

The strikes are the latest blows in a conflict that has spread into the Middle East since October 7, when the Iran-backed Palestinian group Hamas stormed Israel from the Gaza Strip.

Tehran-backed groups declaring support for the Palestinians have entered the fray across the region: Hezbollah has fired at Israeli targets at the Lebanese-Israeli border, Iraqi militias have fired on US forces in Iraq and Syria, and the Houthis have fired on shipping in the Red Sea and at Israel itself.

Iran has so far avoided any direct role in the conflict, even as it backs those groups.

Sullivan declined to be drawn on whether the United States might attack sites inside Iran, something the US military has been very careful to avoid.

He told CBS that Friday's strikes were "the beginning, not the end, of our response, and there will be more steps - some seen, some perhaps unseen".

"I would not describe it as some open-ended military campaign," he said.

Saturday's strikes in Yemen hit buried weapons storage facilities, missile systems, launchers and other capabilities the Houthis have used to attack Red Sea shipping, the Pentagon said, adding it targeted 13 locations.

The Houthi military spokesperson Yahya Sarea said the strikes "will not pass without a response and consequences".

Another Houthi spokesperson, Mohammed Abdulsalam, indicated the group would not be deterred, saying Yemen's decision to support Gaza would not be affected by any attack.

The Houthis did not announce any casualties.

The Yemen strikes are running parallel to the unfolding US campaign of retaliation over the killing of three American soldiers in a drone strike by Iran-backed militants on an outpost in Jordan.

With regard to Gaza, Sullivan said that humanitarian issues in the Palestinian enclave will be a top priority for top US diplomat Antony Blinken on his current trip to the region.

Blinken was en route to the Middle East in a trip that will include stops in Israel, Egypt, Qatar, Saudi Arabia and the West Bank this week.

Jake Sullivan still can't acknowledge that US support for the Israel/Gaza war has expanded into a wider war in the Middle East

— Michael Tracey (@mtracey)

Sullivan said a deal for the Palestinian group Hamas to release its remaining hostages during a humanitarian pause is in the US national interest.

He also stated that the United States believes it is vital to secure a deal to release the remaining hostages Hamas took during its attack, including American hostages, and an accompanying humanitarian pause.

The ball is in the court of Hamas when it comes to such a deal, Sullivan said, noting that the Israelis have put forth a proposal.

A top priority for Blinken on this trip will be to get humanitarian help for Gazans who are in dire straits after months of military aggression from Israel since October 7, according to the national security advisor.

Sullivan emphasised that "the needs of the Palestinian people are something that are going to be front and center."