Yemen's Houthi rebels have confirmed in writing to the UN secretary general their commitment to UN resolutions aimed at ending the country's conflict, BBC News reports.

In a letter obtained by the BBC, Houthi representatives pledge to adhere to a seven-point peace plan brokered by the UN during talks in Muscat, Oman.

The letter follows a verbal commitment to the resolutions issued last month.

The UN estimates nearly 4,900 people, including 2,355 civilians, have been killed in the conflict in Yemen.

Addressed to Ban Ki Moon, the letter commits to the seven Muscat principles, which include a ceasefire, the removal of armed militias from the cities and the return of the government to the capital, Sanaa.

Yemen's President Abdrabbuh Mansour Hadi has insisted Houthi fighters pull back from territory seized over the past year before an agreement can be reached.

In the letter, the Houthi representatives, known officially as Ansar Allah, call the peace plan an "important and fundamental ... step towards the resumption of the political process".

"We, from our side along with other parties, commit to these seven points as one unified bundle," it says, adding: "We welcome the UN call for all sides to return to the table of dialogue."

The letter criticizes the government, alleging it has "not shown any positive reciprocity" with the UN peace process.