Yemen peace talks opened in Kuwait City on Thursday after being delayed for three days, Kuwait's state television reported.
The Iran-backed Houthi rebels and allied representatives of ex-president Ali Abdullah Saleh arrived just hours before the talks finally started.
The talks have continued among representatives of Yemen's government, Iran-backed Houthi rebels and their allies from ex-president Ali Abdullah Saleh's party, along with UN Special Envoy Ismail Ould Cheikh Ahmed.
The talks, originally scheduled to start on Monday, were delayed following accusations by the Houthi rebels of truce violations and divisions related to the road map on the table.
Yemeni President Abedrabbo Mansour Hadi had sent a message to the UN envoy refusing "rebel conditions to modify the agreed agenda", said a member of the government delegation.
Mahdi al-Mashat, a representative of rebel leader Abdulmalik al-Huthi, stated Wednesday the rebels had been assured the agenda for the talks would be "clear and tackle issues that could help achieve peaceful solutions".
Writing on social media, Mashat warned however that "we will have the right to suspend our participation" if the assurances are not met.
During an opening speech, Kuwait's Foreign Minister Sheikh Sabah al Khalid al Sabah, described the talks as "a historic opportunity" to end the war and urged Yemenis to "turn war into peace and backwardness into development."
"War will only lead to more devastation, losses and displacement of people," he said.
The talks are mainly based on the UN Security Council resolution 2216 which calls on Houthis to withdraw from the areas they captured since 2014 and return the heavy weapons in their possession back to the Yemeni government, according to UN Special Envoy to Yemen Ismail Ould Cheikh Ahmed.
"The choice today is one of two options: a safe homeland that ensures security for all of its citizens... or remnants of a land whose sons die everyday," Cheikh Ahmed indicated in an opening speech.
Rebels demand end of US-led coalition operations
Rebels are demanding authorities to end Saudi-led coalition attacks and lift a naval blockade on Yemen, diplomats say.
They also call for UN sanctions against some of their leaders, including Saleh, to be lifted.
The Turkish government announced on Thursday that it has frozen the assets of former Yemeni president Ali Abdullah Saleh in line with a decision made by the United Nations Security Council.
All of Saleh's assets in Turkish banks and other financial institutions were frozen, the government said in its Official Gazette.
Investigators appointed by the UN have told the Security Council that they suspect Saleh of amassing as much as 60 billion dollars, equivalent to Yemen's annual GDP during his long rule.
A UN-brokered ceasefire has sought to facilitate the negotiations in Kuwait, but it has repeatedly been violated by both sides. Sanaa, Taiz, Marib and Jouf cities have seen most of the ceasefire violations.
Both warring parties have accused each other of violating the April 11 ceasefire.
On late Monday, 13 people - five soldiers and eight rebels - died in clashes which continued through Tuesday in Marib, the pro-government military sources said.
United Nations Secretary General Ban Ki-moon urged Hadi’s government and the Houthi rebels and their allies to "engage in good faith" with his envoy on the conflict so that peace talks could start without further delay.
Yemen has remained in turmoil since September 2014, when the Houthi rebels, backed by Iran, overran the capital Sanaa and other parts of the country, forcing Hadi and his government to flee to Saudi Arabia.
Saudi Arabia and its Gulf allies began a military campaign in March 2015, aimed at restoring President Hadi back to power.
The Saudi-led coalition was able to push Houthi rebels out of the southern port city of Aden last July, but Houthis still control the capital, Sanaa.
The UN said that the conflict has killed more than 6,400 Yemenis and displaced 2.8 million from their homes.
Al Qaeda and DAESH have also exploited the war to widen their influence in the poorest country of the Arabian peninsula.