Thousands have been protesting against the takeover for a second day, in cities across Yemen.
On Friday, the Shia rebels said they were dissolving parliament and setting up an interim government.
The UN Security Council has warned of unspecified further steps if the group do not immediately return to talks.
The Houthis took control of parts of the capital Sanaa in September last year, forcing the resignation of President Abed Rabbo Mansour Hadi in January.
Defending the move, Houthi leader Abdul Malik al-Houthi said on Saturday that the declaration was "a historic, necessary and important step" to prevent a power vacuum in Yemen.
He added: "Our hand is extended to every political force in this country. The space is open for partnership, co-operation and brotherhood."
During protests in Sanaa on Saturday, Houthi gunmen fired into the air to disperse demonstrators. A bomb exploded outside the presidential palace, wounding three people.
There were also protests in at least three other Yemeni cities, with demonstrators calling the Houthis actions a coup.
Meanwhile, a rally in support of the Houthis took place in at a stadium in Sanaa.
The Gulf Cooperation Council, made up of Yemen's neighbours and led by Saudi Arabia, has also expressed alarm.
Iran has been accused of backing the Houthis, something both have denied, and analysts say the GCC's opposition signals Sunni Muslim hostility to the Houthis.
The Houthi's political takeover comes after a deadline they set for political parties to resolve the crisis expired, and UN-brokered peace talks failed.
Yemen has been riven by instability since protesters inspired by the Arab Spring forced the overthrow of President Ali Abdullah Saleh in 2011, who is believed to have been backing the Houthis.
The country is also fighting an al-Qaeda insurgency with the help of US drones. Despite the takeover, the US said it was continuing to work with Yemeni on counter-terrorism.
Yemen's Houthi rebels say they are open to working with other political factions, after taking over power in a move denounced by rivals as a coup.