Eleven days since Saudi-led air strikes began pounding Yemen, both parties have indicated a willingness to talk but have set incompatible terms for negotiations.
The Houthis are willing to sit down for peace talks if the air campaign is halted and negotiations are overseen by "non-aggressive" parties.
Saudi Arabia's King Salman said the kingdom was also ready for a political meeting of Yemeni parties, but under the auspices of the Gulf Cooperation Council (GCC).
Five out of the six GCC member states are part of the military coalition bombing Yemen.
The Houthis are against the return of former president Abd-Rabbu Mansour Hadi, who is backed by the Saudis.
A senior Houthi member, Saleh al-Sammad, who was an adviser to Hadi, told Reuters that the Yemenis oppose the return of Hadi who is backed by the coalition.
Sammad added that he wanted the dialogue sessions aired to the Yemeni people so that they can know "who is the obstructer".
He denied the Houthis want control of the south and said they were focused on confronting the threat from al- Qaeda.
Media experts are sceptical of any dialogue, says Al Arabiya News Channel, who see the call for dialogue as an indication the Houthis are collapsing.
Oman, which often brokers peace deals in the Gulf and has stayed clear of the Saudi-led military operations, has refrained this time saying that neither side was ready for negotiations.
Coalition warplanes and ships have been bombing the Iran-allied Houthi forces after UN brokered talks between the Houthis and Hadi failed.
The Houthis have, meanwhile, arrested more than a hundred members from a rival Islamist Sunni political party, including two leaders in an overnight roundup, the party said in a statement.
The Islah party, the Muslim Brotherhood's branch in Yemen and a traditional power player in Yemen, had declared its support for the coalition bombing campaign against the rebels and their allies.
The southern city of Aden continued to witness clashes between Houthi rebels and their army allies with local militias ending in many casualties on both sides. Gun battles and heavy shelling ripped a downtown district near the city's port.
Air strikes fail?
Houthi forces have been battling to take Aden from fighters loyal to Hadi, advancing to the city centre despite the air strikes.
The fighting has so far failed to inflict any decisive defeat on the Houthis, or their supporters, say agency reports.
"There are bodies in the streets and we can't get close because there are Houthi snipers on the rooftops. Anything that gets near they shoot at, and the shelling on Mualla has been indiscriminate," a medic told Reuters.
Local stores have largely run out of produce, milk and other foods due to blocked routes to agricultural hinterlands.
In the eastern coastal town of Mukalla, tribesmen have managed to push al-Qaeda fighters out of much of the town just three days after the militants overran it, residents said.
Saudi authorities have decided to demolish 96 deserted border villages to prevent their use by infiltrators from Yemen. Ten villages have already been demolished since Operation Decisive Storm was launched on 26 March.
Houthi fighters seized the capital Sanaa six months ago and launched an offensive in the south, backed by army units loyal to long time ruler Ali Abdullah Saleh.
Saleh's loyalists control elite forces and large combat units in Yemen's military.
Critics of the Houthis allege that the rebels are proxies for regional Shiite powerhouse Iran. Tehran is accused of supplying the rebels with some logistical aid and supplies, but it strongly denies the claim.