Hani Mohammed, Associated Press
Shiite rebels, known as Houthis, attend a protest against Saudi-led airstrikes in Sanaa, Yemen, Friday, April 15, 2016.

SANAA, Yemen — Yemen's Shiite rebels have reversed an earlier decision to boycott U.N.-sponsored peace talks designed to find a way to end the war in the impoverished Arab nation and their delegation was on its way Wednesday, heading to the negotiations, due to take place in Kuwait.

Representatives of the rebels, also known as Houthis, and their allies left the capital, Sanaa, to neighboring Oman en route to Kuwait.

In a statement issued late Tuesday, senior Houthi leader Mahdi al-Mashat said the movement has received assurances from Kuwait and Oman that there will be no more violations of a week-long cease-fire by the Saudi-led coalition, which has been carrying out airstrikes against the Houthis.

"We reserve the right to suspend our participation if the promises are not kept," said al-Mashat. He and Houthi spokesman Mohammed Abdel-Salam are the most senior delegates in the rebel team.

"The forces of aggression then will have to assume full responsibility for the consequences of their failure to honor their commitments," al-Mashat added.

The talks, which had originally been scheduled to get underway Monday, are aimed at finding ways to resolve the year-long conflict between Yemen's internationally recognized government, backed by the Saudi-led coalition, and the Houthis and their allies.

A U.N.-brokered cease-fire announced earlier this month has sought to facilitate the negotiations in Kuwait, though it has repeatedly been breached by both sides.

Along with Sanaa, the cities of Taiz, Marib and Jouf have seen most of the cease-fire violations. Security officials said Wednesday that coalition warplanes bombed Houthi positions in Taiz and the province of Marib at dawn Wednesday. There were no reports on casualties and damage immediately available. The officials spoke on condition of anonymity in line with regulations.

Yemen's war has killed thousands and displaced 2.4 million people while the Houthis still retain control in much of the country's northern regions — including the capital, Sanaa. The conflict has also fueled secessionist aspirations among the Southerners' for independence, which they had before Yemen was unified in 1990.