Shiite rebels holding Yemen's president captive in his home have reached a deal with the US-backed leader to end a violent stand-off in the capital Sana'a.

The agreement promised to give the rebel Houthi movement more say in the affairs of the Arab world's poorest country in exchange for the group removing its fighters from President Abed Rabbo Mansour Hadi's home.

However, the deal left unanswered who really controls the country and how much power is still held by Mr Hadi, a key ally in US efforts to battle Yemen's local al Qaida branch.

In the deal, the Houthis also agreed to release a top aide to Mr Hadi whom they had kidnapped in recent days.

The agreement included a clause which would answer the rebels' demands to amend the constitution and expand their representation in the parliament and in state institutions. It also included promises to ensure better representation for Yemen's southerners as well, the deal said.

The agreement also calls on Mr Hadi to shake up a commission tasked with writing a draft constitution to ensure bigger representation for the Houthis.

The draft constitution has proposed a federation of six regions, something the Houthis reject. The agreement reached also ensures Yemen would be a federal state, but does not mention the six region proposal, saying controversial issues will be further discussed.

The agreement, while addressing the immediate Houthi takeover and security concerns in the capital, leaves the contentious political issues unresolved.

The Houthis, who took control of the capital in September, say they only want an equal share of power, while critics say they prefer presence of Mr Hadi as a symbolic leader while they keep a grip on power. Critics also say the Houthis are backed by Shiite power Iran, something they deny.

The increasingly weakened leadership and power vacuum are setting the stage for al Qaida in Yemen, which claimed the recent attack on the French satirical newspaper Charlie Hebdo and failed assaults on the US homeland, to grow more powerful in the chaos.