Arab media is reporting that the former president's supporters have gained control of key government installations in the capital, including the defense ministry, the interior ministry and Sana'a Airport.
"I call on our brothers in neighbouring countries ... to stop their aggression and lift the blockade ... and we will turn the page", the former president said in a televised speech. The coalition had also imposed a blockade on the country, allowing occasional humanitarian access, with the aim of reinstating the internationally recognised government of Mr Saleh's successor, Abed Rabbo Mansour Hadi.
The Qatari regime had been attempting since Friday to mediate a rapprochement between the Houthi militias and former Yemeni President Ali Abdullah Saleh's forces, an informed source told Asharq Al-Awsat on Saturday.
Street fighting in the war-wracked country comes amid heightened regional tensions, most notably after Houthi rebels early last month launched a missile that was intercepted near the Saudi capital.
Saleh, who was forced to step down by a 2011 mass uprising against his 33 years in office, said Yemen's parliament, which is dominated by his GPC party, was the only legitimate power in the country and was ready for talks with the coalition.
But Saleh's message didn't sit well with the Houthis, whose spokesman called his remarks "a coup against our alliance and partnership".
The coalition accuses Saleh of having betrayed his Arab neighbours by joining the Houthi-led forces they say are aligned with non-Arab Iran. 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.
In a televised address, Saleh called for new relations with the Saudi-led coalition, which he and the Houthis have been battling for nearly three years (since March 2015).
"The GPC appealed to the army and security forces to remain neutral in the conflict".
The Houthis' Ansarullah group, in a statement issued on its Twitter account, described the clashes as "regrettable".
Stressing that Yemen's interests lie in avoiding sedition, the Houthi leader called on citizens and tribal fighters to focus on the battle against the invading Saudi regime and stay away from any provocative acts.
In response to Saleh's speech, Houthi leader Abdel-Malek al-Houthi stressed the need for dialogue in another televised appearance in Saturday, and called on Saleh to "be more mature".