SAN’A, Yemen—The minority group whose militants have overrun Yemen’s capital said it would take power by force and impose its own political order if a consensual arrangement to end a political standoff isn’t reached by Wednesday.

The Houthis—who desire a greater role in the government—met with other Yemeni factions and a United Nations envoy, Moroccan Jamal Benomar, in the aftermath of President Abed Rabbo Mansour Hadi ’s abrupt resignation on Jan. 22.

Bilateral talks on a power-sharing arrangement proved fruitless, however, prompting Houthi leader Abdul Malik al Houthi to call a three-day conference that started Friday. He then extended the conference, held at a converted indoor sports stadium San’a, until Wednesday.

As the new deadline for a deal approaches, Yemeni political leaders say little consensus has been achieved on how the country should be run.

Houthi leaders are critical of U.N. moderation and wary of foreign interference.

“Some political factions want to compromise but on condition we let them continue in the corruption they are involved in,” said another Houthi leader, Abdullah Shaban. “We are witnessing a revolution, and that’s impossible.”

Opponents say the Houthis lack experience at governing, but still want to call the shots. The Houthis, who are trying to reinvigorate the Zaidi offshoot of Shiite Islam, stormed the capital in September, but opponents say they have been reluctant to take power unilaterally because of their inexperience and the potential for unrest.

“The Houthis are in control of Yemeni politics, but they want to involve others in decision-making on their agenda,” said Mohammed Abulahoum, the president of the Justice and Building party, which has been involved in the U.N.-brokered talks. “If the Houthis wanted to rule Yemen, they could have done that last week, but they know they are amateurs and have a lot to learn.”

Thousands of Yemenis have taken part in daily protests, angered by the political deadlock. Ever since armed Houthi militants took control of key government buildings and the presidential palace in the days before Mr. Hadi’s resignation, the president has been kept under house arrest, but allowed to receive visitors. While he has stepped down, his resignation isn’t yet valid under Yemeni law pending a majority vote in Parliament.

Once held up as an example of how an autocratic Middle Eastern regime could transition successfully to democracy after the Arab Spring, Yemen’s political system is now in tatters, with prospects for unity and stability increasingly grim. Mr. Hadi succeeded longtime leader Ali Abdullah Saleh in 2012 as part of a political deal brokered by the U.N. and Persian Gulf countries.

The growing uncertainty in Yemen is of concern to the U.S., which has long cooperated with Mr. Hadi’s government on counterterrorism operations against Yemen’s al Qaeda in the Arabian Peninsula, or AQAP. AQAP claimed responsibility for January’s deadly attack on the Paris offices of satirical magazine Charlie Hebdo.

Amid the political turmoil of recent months, the U.S. has opened indirect lines of communication with the Houthis, who are also enemies of AQAP, said officials on both sides. The U.S. has continued to carry out drone strikes targeting AQAP after Mr. Hadi’s resignation.

Yemeni politicians say the two most prominent options on the table in their talks with the Houthis are the delegation of presidential powers to a council with members representing different factions or the continuation of a parliamentary track, beginning with a vote on Mr. Hadi’s resignation.

The Houthis favor either the presidential council or scrapping the government and constitution, both of which would allow them to carve out more power for themselves.

Factions aligned against the Houthis favor the second option, essentially preserving the political order that existed before militants took the capital.

An adviser to Mr. Hadi said the president refuses to take a role in the future unless the Houthis withdraw from San’a, saying the people of southern Yemen wouldn’t accept their presence. The Houthis’ power base lies in Yemen’s northern provinces, but their militants have spread increasingly southward in recent months.

“It’s a Houthi coup, and the world knows that,” the adviser said. “That’s why Houthis are seeking a political deal. Any side that backs the Houthis in any deal will partner with them in their coup against an elected president.”

Mr. Abulahoum said Yemeni parties were reluctant to accede to Houthi political proposals, partly because doing so would legitimize what many of them describe as an illegal coup. Meanwhile, numerous political factions have withdrawn from the U.N. talks, and Mr. Abulahoum said Mr. Benomar, the U.N. envoy, had lost the trust of Houthi opponents.

The Houthis made a new proposal late Tuesday that would give dozens of seats in Parliament to Houthis ahead of new elections, something a senior Houthi official said could serve as a stopgap to end the crisis.

But Mr. Shaban, the Houthi leader, said time for compromise was running out. Houthi militants began to close roads in San’a on Tuesday, in apparent preparation for their planned takeover should the talks fail.

“We want all sides to participate in the decision-making, but if they do not reach a deal by Wednesday, we will take lead and show them how to rule,” Mr. Shaban said.

WSJ