Yemen's Huthi rebels accused ex-president Ali Abdullah Saleh Saturday of staging a "coup" against their fragile alliance, after the strongman said he was open to talks with the Saudi-led coalition fighting them.

"Saleh's speech is a coup against our alliance and partnership ... and exposed the deception of those who claim to stand against aggression," a Huthi spokesman said in a statement carried by the rebels' Al Masirah TV.

Violence in Sanaa has left at least 40 fighters dead or wounded since Wednesday, rebel chief Abdul Malik al-Huthi said, as Saleh loyalists and rebel fighters continued to clash on Saturday afternoon.

Tension between Saleh and Huthi has been rising in recent months. Saleh has accused the Huthis of seeking to monopolise power and the rebels have accused the strongman of treason over his suspected contacts with Saudi Arabia.

Saleh on Saturday said he was ready to "turn the page" with a rival Saudi-led coalition on condition Riyadh and its allies lift a blockade on the impoverished country.

The coalition imposed the blockade last month after Saudi Arabia intercepted a missile fired into its territory by the Huthis, whose fraught alliance with Saleh now appears to be crumbling.