Houthi rebels have pushed into Yemen's capital Sanaa after clashing with government-allied forces in the city's northwest outskirts.

The advance by the Shia rebels comes after weeks of unrest in the city where the Houthis have blocked the road to the main airport and staged anti-government sit-ins at ministries.

Al Jazeera's Hashem Ahelbarra, reporting from Sanaa on Thursday, said the rebels were in total control of the Shamlan and Wadi Dhahr districts on the outskirts, and were moved towards the heart of the city.

"Hundreds and hundreds of Houthi fighters are now in the capital," he said, adding that the regular security forces appeared to be standing on the sidelines of the fighting between the rebels and pro-government Sunni fighters.

In the last few days, the Houthis have been targeting buildings owned by the Sunni Islah party, including the Iman University, which has been surrounded..

"This is something very serious in a country that is divided along sectarian lines," our correspondent said.

"This could push the Islah party to mobilise its own people and that could result in an all-out sectarian war here in the capital."

Residents of Shamlan district told the Reuters news agency that the Houthis were advancing along Thalatheen Street, a major route into the western edge of Sanaa.

A military source said Houthi fighters had also attacked an army camp on the southern entrance of Sanaa, but soldiers repelled the assault.

Decade-long conflict

The fighting has further destabilised an impoverished country also struggling to overcome a secessionist movement in its south, the spread of an al-Qaeda insurgency and other threats.

The Houthis, who belong to the Shia Zaidi sect of Islam, have been involved in a decade-long conflict with the Sunni-dominated government, fighting for more control and territory in the north.

In recent weeks, Houthi protesters have been encamped in Sanaa, calling for the overthrow of the government and the restoration of subsidies cut by the state in July as part of economic reforms.

At least 50 people have been killed in clashes involving Houthi fighters in different parts of the country since Tuesday.

Critics say the Houthis are trying to grab power and carve out a semi-independent state for themselves in the north - something they deny.

The UN special envoy to Yemen met Houthi leader Abdulmalek al-Houthi in Yemen on Wednesday to try and find a way out of the conflict.

The three-hour meeting was "constructive and positive", Jamal Benomar was reported as saying.