Powerful figures from the country's military and political sectors have been included in the eight-member council, with some having fighters on the ground in the conflict.
“Our first option is peace, but we are ready for war,” Abdullah Al Alimi, one of the council's members and Mr Hadi's former chief of staff, told AFP in the Saudi capital Riyadh.
“We believe the council is in a position, with the coalition support, to score a decisive military victory.”
Mr Hadi's internationally recognised government had been locked in conflict for seven years against the Iran-backed Houthis, who control the capital Sanaa and most of the north despite a Saudi-led coalition's military intervention, launched in 2015.
The war has killed hundreds of thousands directly or indirectly, causing what the UN calls the world's worst humanitarian crisis, with millions on the brink of famine.
Mr Hadi's April 7 announcement handing power to the council came at the end of talks in the Saudi capital Riyadh that brought together anti-Houthi factions but were boycotted by the Houthis themselves.
The developments followed the start of a renewable two-month truce that has brought a rare respite from violence and led to cautious hopes the war could finally end.
Mr Hadi said the council would be given the task of “negotiating with the Houthis for a permanent ceasefire".
“We hope the dire situation in Yemen will make people have a desire to leave personal and partisan interests behind in pursuit of peace,” said Mr Al Alimi.
He said council leaders are due to meet in the coming days with UN special envoy to Yemen Hans Grundberg, who last week visited Sanaa for the first time during his mandate and held talks with Houthi leaders.
After meeting Mr Grundberg, the council will travel to Yemen to be sworn in, though Mr Al Alimi refused to specify exactly where.
The council has not yet decided how long it will give the Houthis to join talks, Mr Al Alimi said.
The UN on Monday said the Houthis had agreed to stop the recruitment and use of child soldiers, and to end attacks on schools or hospitals or otherwise risk the safety of youngsters.
Virginia Gamba, the UN’s envoy on protecting children in war zones, said the Houthis’ agreement to a UN action plan was a “positive and encouraging step”.
Under the deal, the Houthis will clean their ranks of children within six months.
More than 10,200 children have been killed or maimed during seven years of grinding conflict and nearly 3,500 have been forced to fight, the UN says.
The Houthi rebels refused to participate in the negotiations in Riyadh, which they consider enemy territory, but Mr Al Alimi said future talks could take place in a more neutral location such as Oman.
So far, however, the Houthis have been dismissive, denouncing the new council.
A Saudi-led coalition entered the war in March 2015 at the request of Mr Hadi’s government after the rebels pushed the government into exile.
If the push for peace goes nowhere, the newly aligned anti-Houthi forces are in a position to pursue “a concerted multi-front campaign” against the rebels — provided the council's diverse membership can hold together — said Peter Salisbury, senior Yemen analyst for the International Crisis Group.
“They (the leadership council) have the potential to more aggressively pursue peace and more aggressively pursue war, and the most likely outcome is they do a little bit of one and a little bit of the other,” he said.
- AFP contributed to this report.