The prime minister issued the warning to the group hours after RAF jets took part in a second wave of joint US-UK action against them on Monday night.
Mr Sunak told MPs: “We are not seeking a confrontation. We urge the Houthis and those who enable them to stop these illegal and unacceptable attacks.
“But, if necessary, the United Kingdom will not hesitate to respond again in self-defence. We cannot stand by and allow these attacks to go unchallenged. Inaction is also a choice.”
He also rejected the Yemen-based group’s claims that its attacks have been prompted by the war in Gaza. The prime minister said there was “no link between our actions of self-defence in the Red Sea and the situation in Israel and Gaza”.
He added: “Those who make that link do the Houthis’ work for them. I want to be clear that those here at home who glorify the Houthis’ attacks are glorifying terrorism, plain and simple. They will be met with a zero tolerance approach.” However, despite successfully hitting the designated targets, Mr Sunak admitted that there ”may be a difference between reducing and eliminating” their capability.
The Houthis, meanwhile, warned this latest strike “will not go unanswered or unpunished”.
Since the last UK-US action 10 days ago, there had been more than 12 attacks on shipping by the Houthis in the Red Sea.
Labour leader Sir Keir Starmer gave his support, for what he described as “targeted action”, but again called on ministers to again release their legal justification.
He also said he “totally” rejected the idea that the Houthi attacks were linked to the situation in Gaza, as Mr Sunak faced calls from left-wing Labour MPs, including former shadow chancellor John McDonnell, for the UK to back calls for an immediate ceasefire.
Sir Keir was not told in advance of the latest round of strikes, despite being informed when a similar decision was taken earlier this month.
Mr Sunak’s official spokesman said the government’s preference was to inform the opposition leader, adding “that wasn’t a possibility in this instance”.
Officials say the joint operation by British and American warplanes took out Houthi missile storage sites and launchers.
Monday’s strikes were significantly smaller in scale than the first joint operation, which hit as many as 60 different targets spanning the length and breadth of Houthi-controlled Yemen.
Despite those strikes, the Houthis have continued to target ships along the vital Red Sea and Gulf of Aden trade routes. The Houthis initially said they were targeting vessels linked to Israel in solidarity with the Palestinians suffering in Gaza, and have since expanded their missile attacks to include British and American ships.
In a joint statement, the governments of the US, UK, Bahrain, Australia, Canada and the Netherlands said the “precision strikes” were “intended to disrupt and degrade the capabilities that the Houthis use to threaten global trade and the lives of innocent mariners”.