The Houthi military spokesperson said the group will announce in the coming hours a broad operation deep into Saudi territory.
The Saudi energy ministry said concerned authorities were dealing with the repercussions of the attacks.
"The needed measures will be taken to ensure the safety of the facilities and workers and the continuation of work according to the approved operational plans," said the ministry.
Spokesperson Yahya Saree said on Monday that Riyadh had taken "escalatory steps" by conducting airstrikes on Yemen, and warned that Houthi strikes would not go unanswered.
The Saudi-led coalition did not announce any recent strikes on Yemen, but the Saudi-backed Yemeni government has in recent days mounted an offensive on multiple fronts against the Houthis in Yemen.
The coalition vowed to respond firmly to the latest outbreak of hostilities, saying the latest escalation against the de facto OPEC leader was "dangerous".
"The coalition will take all necessary operational measures to deter this terrorist militia and resolutely confront its hostile approach," Colonel Turki al-Malki said in a statement on X.
The Houthis, who control the most populous parts of Yemen and much of the north, have been launching attacks towards Saudi Arabia since they declared a naval blockade against Riyadh in July, with strikes targeting its vessels in the Red Sea.
Oil prices rise as regional tensions intensify
The flare-up in violence between Saudi Arabia and the militant group came as tensions mounted between the United States and Iran as the wider Middle East conflict sent oil prices soaring with diplomatic negotiations stalling.
Brent crude futures LCOc1 rose $1 to $98/BBL after the Saudi energy ministry statement, while U.S. crude futures CLc1 rose over $2 to $93.65/BBL.
On Monday the Financial Times newspaper said Aramco's Jazan oil facilities were hit in new strikes, and the damage was being assessed. Reuters was not immediately able to verify the report and Aramco 2222.SE has not commented.
Attacks halt operations at Saudi energy facilities
DUBAI, Sept 8 (Reuters) - Operations at some energy facilities in Saudi Arabia, the world's top oil exporter, were halted on Tuesday following attacks by Yemen's Iran-aligned Houthis that wounded 73 people, in what Saudi authorities described as a dangerous escalation.
Fires erupted at the sites and several people were injured as firefighting and other emergency teams rushed to contain the blazes and assess the damage, the Saudi energy ministry said.
The Houthis attacked the southern cities of Abha, Khamis Mushait, Jazan and Najran, the Saudi-led coalition in Yemen said in an earlier statement, adding that the injured included women and children.
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