Sheikh Sabah al-Ahmad al-Sabah, whose country is hosting the talks, called on the two sides to continue negotiating to "reach positive results", AFP reported.
The appeal came after the emir met separately with the two delegations and the UN envoy, in an attempt to salvage the talks that began four weeks ago.
Senior officials from Kuwait have repeatedly mediated and sought to prevent the collapse of the negotiations aimed at ending nearly 14 months of bloodshed.
The United Nations estimates that more than 6,400 people have been killed and 2.8 million displaced in Yemen since March last year.