Hundreds of people have died in northern Yemen, with the UN estimating that 55,000 people, mostly women and children, have fled their homes since the army began its offensive on August 11.
The Houthi fighters are concentrated mainly in the Saada and Amran provinces.
They are known as Houthis after their late leader, Abdul-Malek's brother Hussein Badr Eddin al-Houthi, a Zaidi leader who was killed by the Yemeni army in September 2004.
An offshoot of Shia Islam, the Zaidis are a minority in mainly Sunni Yemen but form the majority in the north. Only a small minority of Zaidis are in involved in the Houthi uprising.
The government accuses the Houthi fighters of seeking to restore the Zaidi Shia imamate which was overthrown in a 1962 coup that sparked eight years of civil war.
The Houthis say they are fighting to defend their community against government aggression and marginalisation.
Ali Abdullah Saleh, the Yemeni president, has brushed aside calls for dialogue.
The fighting in Yemen's north on Wednesday coincided with fresh unrest in the south.
Two people were killed in Daleh after fighting broke out when security forces confronted protesters who took to the streets to demand the release of people arrested during recent unrest, witnesses said.
Hundreds of protesters took to the streets in Zinjibar, the capital of Abyan province, carrying pictures of the south's exiled leaders and shouting "revolution, revolution", witnesses said.
The south, which was a separate country until it unified with the north in 1990, complains that it is discriminated against by the Saana government.
|The government is worried about separatist sentiments growing in the south [AFP]
Abdallah Al Faqih, a political analyst in Yemen, told Al Jazeera: "The southerners were turned into second-class citizens, they were marginalised politically, socially and economically and they want their things back."
"If the regime does not react decisively and in a timely manner, we will have secession as a real cause, because if you kill people forget about unity."
Around 40 people have been killed and hundreds arrested in clashes with security forces since April in the impoverished south.
The government has demanded that Tareq al-Fadhli, a prominent tribal leader and a former important ally of President Saleh, surrender or leave the country, sources said.
The government suspects that al-Fadhli is the leader of the southern independence movement.
Hashem Ahelbarra, Al Jazeera's correspondent in Yemen, said: "Despite a war in the north, and a secessionist movement in the south, President Saleh seems unwilling to cave in to demands by the southerners and the Houthi rebels for power sharing.
"This is a defiant stance that will further deepen Yemen's political crisis."