Houthis and Saleh loyalists jointly overran Sanaa and much of the country in 2014, forcing the internationally recognized government of President Abd Rabbuh Mansour Hadi to flee to Saudi Arabia.
"We will deal with them in a positive way and what happened to Yemen is enough", he added.
"The uprising in Yemen's capital Sanaa is the sign of an awakening of the nightmare", UAE's Minister of State for Foreign Affairs Anwar Gargash said on Twitter.
Saleh stepped down after 33 years in office in 2012, following months of Arab Spring protests against his rule, but remained leader of the General People's Congress Party (GPC), the country's largest political party.
The United Nations has warned that the country faces mass starvation unless the Saudi-led coalition allows more food aid to enter the impoverished country.
Former Yemeni President Ali Abdullah Saleh - whose supporters are now in a shaky alliance with the Houthi rebels in the fight against the Saudi-led coalition - tossed an olive branch on Saturday to Riyadh, saying he is open to talks with the coalition and ready to "turn the page".
The coalition accuses Saleh, who heads the General People's Congress party, of betraying his Arab neighbors by joining forces with the Houthi rebels.
"It is not odd or surprising that Saleh turns back on a partnership he never believed in", the group's political bureau said in a statement.
Residents of Yemen's capital, Sanaa, are used to the sounds of gunfire, but in the last four days they've had to adjust to new faultlines in the conflict.
Saleh has however rejected the mediation and Doha therefore failed in seizing control of the situation in Yemen and reaching any form of calm or agreement. There has been no official word on casualties but the International Committee of the Red Cross (ICRC) said that dozens were killed and hundreds were wounded in the fighting. Both sides have reported that at least 16 people were killed in the fighting, which began on Wednesday when armed Houthi fighters entered the main mosque complex, firing RPGs and grenades.
The head of the Houthis' Ansarullah group warned that the biggest victor from what he described as Saleh's "sedition" was the Saudi-led coalition.
Saudi Arabia has been locked in a fight with the Houthi rebels since it joined the Yemen war in 2015.
Meanwhile, Houthi leader, Abdel-Malek al-Houthi, called for dialogue with Saleh and his rebel forces to end the growing violence between the two factions.