Honduras' president-elect Xiomara Castro made a last ditch attempt late Wednesday to solve a congressional crisis with hours left before her inauguration.

Last week two rival factions within her left wing Libre party elected their own duelling presidents of Congress.

Castro backs the claims of Luis Redondo of her coalition partner Savior Party of Honduras (PSH).

But Jorge Calix, a deputy within her own Libre party, has led a band of close to 20 rebels, with support from the right wing National and Liberal parties, to launch a rival claim.

Late on Wednesday, Castro tried to break the impasse by offering Calix a role in her cabinet.

"I proposed to Jorge Calix that he joins my government in the position of Cabinet Coordinator for the sake of uniting in the Reformation of Honduras," Castro wrote on Twitter.

She did not, however, explain what the role entailed, although it appears to be something akin to a chief of staff.

"Thank you President @XiomaraCastroZ, it was a great pleasure speaking with you," said Calix in a reply to her post on Twitter.

"For me and for anyone, it would be a great honor to form part of the government of resistence and national reconciliation. You will soon receive my answer," he wrote.

Honduras president elect Xiomara Castro (right) has made an offer to rebel deputy Jorge Calix (left) in a bid to end a congressional crisis ahead of her inauguration Honduras president elect Xiomara Castro (right) has made an offer to rebel deputy Jorge Calix (left) in a bid to end a congressional crisis ahead of her inauguration Photo: XIOMARA CASTRO'S PRESS OFFICE via AFP

The offer came a day after the two rival factions held competing first sessions presided over by their respective presidents.

Redondo took office as president of the Congress in the building that houses the legislative body.

In parallel and via video link, Calix was also installed as head of Congress by his own loyalist faction.

Calix was joined by around 70 deputies while only around 40 were in the parliament building, although the Redondo faction achieved a quorum as substitute lawmakers stood in for those that were absent.

The crisis broke out last week when a group of Libre dissidents ignored an agreement with the PSH, whose support was key to Castro winning the November elections.

Rival lawmakers came to blows in the dispute.

PSH leader Salvador Nasralla had agreed to withdraw his presidential candidacy and support Castro, in return for the position of vice president and a member of his party being named president of Congress.

But the dissidents argued that Congress should be led by the party with the most members -- Libre has 50 deputies compared to just 10 for the Savior party.

Control of parliament is key to Castro's anti-corruption and political reform platform in a country battered by poverty, migration and drug trafficking.