Houthi fighters ride in a truck on a street leading to the Republican Palace in Sanaa Reuters

Houthi militiamen have replaced presidential security officers outside the private home of Yemen's President Abd-Rabbu Mansour Hadi as the battle for power in the country continues.

The presidential guard was nowhere to be seen at the compound after clashes with the Houthi gunmen earlier in the week.

"President Hadi is still in his home. There is no problem, he can leave," Mohammed al-Bukhaiti, a member of the Houthi political bureau, told Reuters.

The United Nations security council condemned the Shiite militiamen for their attack and said that Hadi was "the legitimate authority" in Yemen and called on all actors in the conflict "to keep the country on track to stability and security".

Elsewhere, the rebels entered Hadi's presidential palace in a step to ensure that they receive a greater share of power in the country's political make-up.

After the fighters had entered the palace, their leader Abdel-Malek al-Houthi said that Hadi had to follow through on the power-sharing agreement signed in September after the rebels seized the capital, Sanaa.

Fears are mounting that, with Hadi trapped inside his residence, he may fall and leave a power vacuum in a country beset by unrest and an al-Qaeda insurgency.

EU foreign policy chief Federica Mogherini said that "all parties must step back immediately from conflict."