"We still stand by our position on dialogue and we demand its continuation despite everything that has happened, on the basis of respect and acknowledging the other," Sammad said.
"We have no conditions except a halt to the aggression and sitting on the dialogue table within a specific time period ... and any international or regional parties that have no aggressive positions towards the Yemeni people can oversee the dialogue," Sammad said, without specifying who they might be.
Sammad added that he wanted the dialogue sessions aired to the Yemeni people "so that they can know who is the obstructer.”
This weekend, Houthi forces rounded up and detained more than 120 members of the rival Islah party, the Yemeni Muslim Brotherhood branch, the Houthis said on their website Sunday.
Also Sunday, Houthi forces advanced to near the port of Mualla, with airstrikes targeting the group's strongholds. Mualla is defended by militiamen of "popular committees" loyal to President Hadi.
But just hours later, they were pushed back by pro-Hadi fighters. A pro-Hadi militia source told Reuters 36 Houthi were killed near the port, while 11 of Hadi's combatants died.
Aden residents reported hearing sporadic gunfire and blasts of rocket-propelled grenades.
Summer Nasser, a human rights activist and blogger, told Al Jazeera that she had to leave her home in Aden because of the fighting.
"Conditions are devastating actually. We've heard shelling by Houthis on homes, civilians killed. There's no electricity, water. I feel like the humanitarian crisis in Aden is actually getting worse by the hour," she said.
Television footage purports to show coalition warships bombing Houthi ammunition supply lines and depots from sea.
Aden, the last foothold of supporters of Hadi, has been shaken by more than a week of fierce clashes between the Shia rebels and Hadi loyalists.
At least 185 dead and 1,282 wounded from the clashes have been counted in hospitals in Aden since March 26, the city's health department director al-Kheder Lassouar said on Saturday. The United Nations says more than 500 people have been killed in the past two weeks in Yemen and nearly 1,700 wounded.
Airstrikes in the southern city of Dhale, close to Aden, killed at least five civilians on Sunday, medical officials told the Associated Press.
Saudi Arabia's King Salman was quoted as saying Monday that the kingdom was ready for a political meeting of Yemeni parties, under the auspices of the Gulf Cooperation Council (GCC). Five out of the six GCC member states are part of the military coalition bombing which is bombing the Houthis.
Houthi fighters seized the capital Sanaa six months ago and last month launched an offensive on the south, backed by army units loyal to longtime ruler Ali Abdullah Saleh.
That prompted Saudi Arabia to launch a campaign of airstrikes on March 26 alongside regional Sunni Muslim Arab allies.
The conflict has turned Yemen into another front in Sunni Muslim Saudi Arabia's proxy war with Shia rival Iran, a struggle which is also playing out in Syria, Lebanon and Iraq.
Tehran denies Riyadh's charges that its arms the Houthis, and Sammad dismissed the accusations as rumors. "Even if there was Iranian support as is being said, it is not an excuse for this flagrant aggression," he said.
Sammad denied the Houthis want control of the south, home to a long-running secessionist movement, and said they were focused on confronting the threat from Al-Qaeda.
"The sons of the south will run their own affairs, and they will have the more prominent role in the coming political scene," he said.
Al Jazeera and wire services