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.

The former world number one, 56, last won the tournament in 2014, but earned a 17-9 victory in front of a raucous crowd at Blackpool's Winter Gardens.
He faces Peter Wright, who beat Daryl Gurney 17-15, in Sunday's final.
"It's my last day here tomorrow and I'm going out with a bang," said Taylor, who is retiring at the end of the year.
Englishman Taylor continued his fine form after thrashing Dutch world number one Michael van Gerwen in the quarter-finals on Friday.
It was 32-year-old Lewis, also of England, who broke first and took a 3-1 lead, but Taylor came back almost instantly to level the match at 3-3.
Despite his superior average going into the second interval, Taylor only led 8-7 with the throw.
But in a repeat of the 2013 final, in which Taylor beat Lewis 18-13, the 15-time champion became the more dominant player as the match progressed.
With Lewis starting to make more mistakes, Taylor raced away to victory.
Taylor told Sky Sports: "My mindset was keep him under pressure and that he will feel it in the last part of the game.
"I knew he was shattered and I had to take advantage, even though I love him."
Wright is through to his first final at the World Matchplay and a win over Taylor would be the biggest prize of the 47-year-old Scot's professional career so far.
He will be looking to improve on his average of 93 in a heated semi-final against Northern Ireland's Gurney, which included some verbal exchanges between the two players.
"We had a little argy-bargy on stage. I was getting grief from the crowd, he wasn't. Then he said something to me when I walked past," Wright told Sky Sports.
"I got over the line anyway and I'm in the final. I'm one game away."
The World Matchplay is considered the second biggest tournament in the sport, after the World Championship.
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.
[NEXT_CONCEPT]
Phil Taylor produced a brilliant semi-final display to beat Adrian Lewis and stay on course for his 16th World Matchplay title.