Yemen's Houthis on Wednesday warned former president Ali Abdullah Saleh, their main ally in the country's war, that he would "bear the consequences" after calling the Iran-backed Houthis "militias".

Fears are now mounting that violence could break out in Sanaa around a rally scheduled for Thursday to mark 35 years since the founding of Saleh's General People's Congress party.

Cracks began to surface this week in the alliance between Houthi chief Abdul Malik al-Houthi and strongman Saleh, allied since 2014 against Yemen's government, with the two exchanging mutual accusations of back-stabbing in televised speeches.

A statement released by the Houthis early on Wednesday hit back at Saleh, calling the ex-president a "traitor" after he dismissed the group as a "militia" in a speech on Sunday.

"We have been stabbed in the back and called a militia, which is treason in its purest form," read the statement.

"What he [Saleh] said crosses the red line ... and he will have to bear the consequences of his words."

Tension has been rising for days in the Yemeni capital, which is jointly controlled by Saleh and the Houthis, and eyewitnesses say armed supporters of Saleh and Houthi have intensified their presence across the city.

Yemen's war, which pits the Saudi-backed government against the Saleh-Houthi alliance, has claimed thousands of lives since 2015 and pushed the country to the brink of famine.

-Agencies