The Iran-aligned Houthis of Yemen vowed to respond to attacks by the United States and Britain but the prospects of these Western strikes igniting a regional war seem limited for now as Tehran seeks to avoid getting sucked directly into all-out conflict.

A response to Houthi attacks in the Red Sea, the strikes further internationalised the conflict that has spread through the region since Hamas and Israel went to war, with Iran's allies also staging attacks from Lebanon, Syria and Iraq.

Iraqi militias responded with new threats against US interests, while Washington declared the Gulf state Bahrain among allies that supported the operation, risking the ire of the Houthis who have a powerful arsenal of drones and missiles.

"It was completely foreseeable that the longer the Gaza war drags on, the higher the risks of escalation and regional conflagration," said Ali Vaez, senior Iran analyst at the International Crisis Group.

"Iran is unlikely to directly enter the fray as long as it has not been directly targeted on its own soil," he added.

But the Houthis could step up their strikes.

"The strikes will not stop the Houthis from further attacks in the Red Sea - if anything, rather the opposite," said Farea Al-Muslimi of Chatham House.

Saudi Arabia, an ally of Bahrain, called for restraint and "avoiding escalation", adding that it was monitoring the situation with "great concern".

Last month, Saudi Arabia's name was conspicuously absent from a list of countries the United States announced as part of a naval coalition protecting Red Sea shipping from the Houthis.

"Part of the reason the Gulf states have been shielded off of these tensions is their better ties with Iran," Vaez said.

NO APPETITE FOR ALL-OUT WAR

The Houthis, who control most of Yemen, have been firing on commercial ships they say are linked to Israel or bound for its ports since November, demanding a halt to the Israeli offensive on the Gaza Strip.

After US and British forces launched dozens of air strikes across Yemen overnight in response, they vowed retaliation, saying five of their fighters were killed.

Iran's foreign ministry said the attacks would fuel "insecurity and instability".

But while Iran continues to back a network of allies from the Mediterranean to the Gulf known as the "Axis of Resistance", two Iranian sources familiar with Iranian thinking said Tehran does not want to get directly involved.

A third Iranian source, a senior official who asked to remain anonymous, said the Houthis were taking their own decisions and "we support their fight, but Tehran does not want an all-out war in the region". It was up to Israel and the United States to stop "their aggression", the official said.

The United States says it has been seeking to prevent war from spreading through the region, including at the Israel-Lebanese border, where the Iran-backed Hezbollah and Israel have been fighting their worst conflict in 17 years.

The United States has accused Iran of being involved operationally in the Houthis' Red Sea attacks. Iran denies any role and says its allies take their own decisions.

Gregory Brew, an analyst at Eurasia Group, said Tehran remained wary of expanding the conflict as it did not want "to be directly exposed to potential retaliation".

"While there are likely to be responses from various Iranian proxies elsewhere in the region, a major escalation from Iran as a response to these strikes is unlikely," he said.

IRAQI THREATS

In Iraq, where Tehran-backed forces have been firing at US forces, the Al-Nujaba militia said the interests of the United States and other coalition members would "not be safe from now on".

An official in another militia, Iraqi Kataib Hezbollah, said the attacks would have "dire consequences for the security of the whole region", including the Gulf: "All the American interests, not only in Iraq and Syria, but in the whole region, will be a legitimate target for our drones and rockets".

In Lebanon, a source familiar with Hezbollah's thinking said responding to the attacks was not its concern but that of the Houthis.

The United States has said the attacks were not intended to escalate tensions and on Friday, the Pentagon said there were no plans to add US forces to the region, and that the strikes had "good effects".

Houthi power in Yemen has grown since the group seized control of the capital Sanaa in 2014 and Saudi Arabia, which intervened the following year amid concern about Iran's growing sway, has recently held peace talks to try to exit the war.

Yemen has enjoyed more than a year of relative calm amid a U.N.-led peace push and Saudi Arabia, seeing regional stability as important to its economic plans, re-established diplomatic ties with Iran last year after years of emnity.

Andrea Krieg of King's College in London expressed doubt over whether the strikes would affect the Houthis willingness or capability to launch attacks, noting they draw on highly mobile infrastructure. "Nine years of Saudi operations in Yemen have shown that the Houthis cannot be deterred," he said.