"We will face all of the incursions on the ground. Our determination will never be dented," Abdul-Malik Badreddin al-Houthi was quoted by al-Masirah on Wednesday.
He added that the kingdom and its allies were exploiting political problems in Yemen in order to occupy the war-torn country’s south.
Houthi noted that Yemen's Red Sea coasts will turn into a graveyard for his those who try to invade the country.
Earlier in the day, Saudi-backed Yemeni forces, loyal to ex-president Abd Rabbuh Mansur Hadi, claimed that they have seized the airport in the port city of Hudaydah from the Houthi Ansarullah fighters.
Brigadier Abdul Salaam al-Shehi, a Saudi-led coalition commander in Yemen's Red Sea coast, said in a video posted by the UAE’s official WAM news agency on Wednesday that the Hudaydah airport is “completely cleared” and “under control.”
The claims were denied by the Ansarullah movement.
The Hudaydah airport lies just eight kilometers from the city’s port, through which three-quarters of Yemen’s imports pass, providing a lifeline for millions of people.
Backed by Saudi-led airstrikes, the United Arab Emirates and allied militants loyal to the former Yemeni government launched the Hudaydah assault on June 13 despite warnings that it would compound the impoverished nation’s humanitarian crisis.
The Houthis and allied armed forces, however, said that they have dealt a heavy blow to the aggressors, inflicting heavy losses on the invaders.
The UN says fierce clashes in the port city have driven 5,200 families from their homes.
The Saudi-led coalition claims that the Houthis are using Hudaydah for weapons delivery, an allegation rejected by the fighters.
World Health Organization worried about Hudaydah
Meanwhile, the World Health Organization has voiced grave concern over the ongoing clashes in and around Hudaydah.
The Incident Manager of the WHO in Yemen also said the agency is importing extra medicines for cholera as well as other standard medical supplies.
Forces from Saudi Arabia and the United Arab Emirates started the invasion on the Houthi-controlled city last week, causing more deaths and destruction to Yemen. Hudaydah is the lone entry point for goods and essentials to the war-battered country.
Saudi Arabia and its allies launched the war on Yemen in March 2015 to reinstall Yemen’s former President Abd Rabbuh Mansur Hadi. The Yemeni Ministry of Human Rights announced in a statement on March 25 that the war had left 600,000 civilians dead and injured until then.
The war and an accompanying blockade have caused famine across Yemen. The United Nations says a record 22.2 million people are in need of food aid, including 8.4 million threatened by severe hunger.
The Saudi aggression has also taken a heavy toll on the country's facilities and infrastructure, destroying many hospitals, schools, and factories.
Since 2016, the impoverished nation has also been grappling with a deadly cholera outbreak, which has already killed thousands of people.
Several Western countries, the US and the UK in particular, are accused of being complicit in the aggression as they supply the Riyadh regime with advanced weapons and military equipment as well as logistical and intelligence assistance.