Yemen's warring parties have pledged to free all child prisoners but have failed to reach agreement on a wider release for the Muslim holy month of Ramadan, the UN envoy said on Monday.

"In the prisoners committee, an agreement was made on the unconditional release of children," Ismail Ould Cheikh Ahmed said in a statement.

There was no immediate word on how many children are held prisoner by the Saudi-backed government or by Iran-backed Shiite rebels and their allies.

The UN envoy had been trying to push the two sides to agree to release half of all their prisoners before Ramadan, which began on Monday.

After almost seven weeks of negotiations, the two sides have failed to make progress on any of the core issues in the UN-brokered peace talks in Kuwait.

The rebels and their allies have held out against demands contained in a UN Security Council resolution for their surrender of heavy weaponry and withdrawal from areas, including the capital, which they have seized since 2014.

The government has resisted proposals for a unity administration with the rebels, fearing it would undermine the legitimacy of President Abedrabbo Mansour Hadi.

The UN envoy said that despite the lack of progress, both sides remained engaged in the talks, which would continue through Ramadan, when Muslims observe a daytime fast.

In the past few days, the talks have been overshadowed by rebel shelling of the besieged government garrison in third city Taez, which killed 11 civilians.

The UN envoy condemned the bombardment and urged both sides to respect a ceasefire that took effect on April 11.

"The attack against a crowded market in Taez is unethical. We condemn the bloody incidents in Taez despite the cessation of hostilities," he said.

There have been no face-to-face meetings between the two sides over the past week. The UN envoy has met with the delegations separately in an effort to come up with bridging proposals.