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New tensions arose between Yemen's Houthi rebels and former president Ali Abdullah Saleh on Thursday after a fresh wave of mutual accusations which threaten their three-year alliance.

Saleh and the Shia Houthi rebels have jointly controlled the capital Sana'a since September 2014, but tensions have been rising since a public dispute between the two in August. 

Saleh's General People's Congress (GPC) on Thursday complained of humiliation at the hands of the Houthis, accusing the rebels of waging an "orchestrated campaign" against the former strongman. 

The GPC said in an open letter to Ansar Allah, the political party led by Houthi chief Abdulmalik al-Houthi, that its ministers had been "humiliated" by the rebels who "lack the will to maintain partnership". 

Ansar Allah in turn accused the GPC of breaking their pact with the Houthis and accepting money from the rival government of President Abedrabbo Mansour Hadi, a statement said.

The party's political leader Salah Sammad accused the GPC of "sapping internal unity" and paralysing the rebel government.

Tensions between Yemen's Houthi rebels and their ally Saleh reached boiling point in August after the Houthis accused the former president of treason after he dismissed the Iranian-backed rebels as "militias".

Saleh as president had fought successive wars against the Houthis but they joined ranks in 2014 to drive the Hadi government out of Sana'a.

The war between the government of President Abd Rabbo Mansour Hadi, backed by the coalition, and the rebel camp has killed more than 10,000 Yemenis since 2015 and pushed the country to the brink of famine.