"The Saudi Arabian cabinet expresses the hope that the uprising of the Yemeni people against the sectarian terrorist Huthi militias supported by Iran will free Yemen of abuse, death threats and the appropriation of public and private property," it said in a statement published on the official SPA news agency.
The statement made no mention of Saleh, who was killed by Yemen's Iran-backed Huthi rebels on Monday.
Saleh, who ruled Yemen for 33 years, was for decades an ally of Saudi Arabia before joining ranks with the Shiite Huthis in 2014.
Saleh's ties to the rebels, strained for months, were dealt a major blow on Saturday when he announced he was again open to talks with Saudi Arabia and its allies, who had been fighting the Saleh-Huthi camp for nearly three years.
Iran -- which Riyadh accuses of arming the Huthis -- on Tuesday also said Yemen would fight back against "aggressors", a jab at Saudi Arabia.
Iran denies it arms the Huthis.