Mohammed Ali al-Houthi, a member of Yemen's Supreme Political Council, delivered the statement on Thursday.
British media disclosed the Royal Navy's withdrawal of HMS Diamond from the Red Sea after facing multiple missile strikes from Yemen.
While specifics on the summoning weren't provided, reports indicated HMS Richmond temporarily assumed duties in the Red Sea, with plans for HMS Diamond's rearming before redeployment.
Footage circulated by Yemeni media purportedly showed a missile striking HMS Diamond in the Red Sea, though the timing remains unspecified.
"As the British warship has exited the region for maintenance, other warships will [be forced to] leave the region," al-Houthi declared.
"All [foreign] warships must vacate the Red Sea, cease attacks on Yemen, and lift the blockade on the country," he asserted.
Yemen has been targeting Israeli vessels, those bound for occupied territories' ports, and British and American warships dispatched to counter Yemeni strikes in the Red Sea.
These actions aim to pressure Israel into halting a Washington- and London-backed war since October 7, 2023.
The Israel war has claimed over 27,840 Palestinian lives, predominantly women, children, and adolescents.