"We seek to stop the spread of conflict and to create the conditions for de-escalation," Sullivan said at the World Economic Forum in Davos, Switzerland.

Sullivan said the course of the conflict with the Iranian-backed rebels depended on "those with influence in Tehran and influence in other capitals in the Middle East".

He said that the United States saw a "pathway" to preventing the Gaza war from escalation into a larger conflict.

"We are eagerly working with partners throughout the region to try and pursue a pathway. But in the meantime, we have to guard against and be vigilant against the possibility that, in fact, rather than heading towards de-escalation, we are on a path of escalation that we have to manage," Sullivan said.

The United States and Britain last week struck Huthi positions in Yemen after the insurgents defiantly attacked ships in the Red Sea in professed solidarity with the Palestinians, disrupting global commerce.

The United States has been the primary backer of Israel in its relentless campaign in the Gaza Strip in response to a deadly attack by Hamas inside Israel on October 7.

While defending Israel's right to respond, Sullivan said that "this does not lessen at all Israel's responsibility to conduct its campaign in a way that upholds international humanitarian law and abides by the moral and strategic necessity to distinguish between terrorists and innocent civilians".

He said that President Joe Biden's administration still wanted a two-state solution with the Palestinians -- an option rejected by hard-right allies of Prime Minister Benjamin Netanyahu -- as well as Israel's integration into the region.

The goal should be "a future where Israelis and Arabs can live in peace, Palestinians have a state of their own and Israel's security is assured", he said.

"I know that in this moment where there's so much anger and pain and so much uncertainty it's hard to imagine, but it really is the only path that provides peace and security for all."