Earlier on Tuesday, the Houthi spokesperson warned Saudi Arabia that any Saudi attack on Sana'a would be met with a "harsh" response.
Houthi-run Al-Masirah TV reported on Tuesday an attack on the Yemen Oil Company in Sana'a shortly after the Saudi-led coalition ordered the evacuation of the facility ahead of a military operation.
The report followed a statement from a Saudi-led coalition spokesperson earlier on Tuesday that a warning would be issued shortly for civilians to evacuate a site in Yemen's Sana'a ahead of a special operation.
Following the reported strikes, Saudi Arabia's cabinet, chaired by Saudi Crown Prince Mohammed bin Salman in Riyadh, said Yemen's Iran-backed Houthi terrorists would face "consequences" for their repeated attacks on the kingdom, Saudi state media reported.
Earlier on Tuesday, the Houthi spokesperson threatened that any Saudi attack on Sana'a would be met with a "harsh" response.
Also on Tuesday, Yemen's Iran-backed Houthi terrorists claimed that Saudi Aramco oil facilities are legitimate targets for the terrorist organization, calling on employees and civilians to evacuate the sites.
Houthi military spokesman Yahya Sarie further called on individuals near any Saudi oil facilities to remain clear of all potential targets.
In an additional statement on Monday, the Houthis threatened to launch a "swift and painful response" against the United States and its regional interests if Washington joined Saudi Arabia's military campaign in Yemen, Houthi political bureau member Mohammed al-Bukhaiti told AFP.
Several Houthi strikes on Riyadh airport kill 14, injure hundreds
The various threats, warnings and statements from Yemen's Houthis come after the terror group killed one person and injured nearly a dozen in an attack on Riyadh's international airport on Sunday.
That attack followed a similar Houthi strike on the airport on Saturday, which killed 13 people and injured over 300.
Following the latest Houthi threats, Turkish President Recep Tayyip Erdogan told Saudi Crown Prince Mohammed bin Salman in a phone call on Tuesday that Turkey would continue to stand by Saudi Arabia amid the Houthi attacks, the Turkish presidency said.
In a statement, the presidency said Erdogan also condemned the Houthi attacks in the strongest terms and told the crown prince that he believed "this challenge will be overcome."
NATO member Turkey, Saudi Arabia, and nuclear-armed Pakistan signed the Mecca Joint Defense Agreement in August, under which an attack on one party constitutes an attack on all.
Shir Perets contributed to this report.