Fighting gripped Yemen's second city Aden on Sunday as the UN envoy arrived in the rebel-held capital Sanaa to press efforts to broker a ceasefire.
Saudi-led warplanes bombed rebel positions, killing eight people, while rebel rocket fire killed six, including a child, officials said.
The dead from the Katyusha fire were Somali refugees who had sought shelter in a kindergarten, medics said.
Aden was the last refuge of President Abedrabbo Mansour Hadi before he fled to Saudi Arabia in March and has been a key battleground ever since.
In neighbouring Lahj province, Hadi loyalists attacked a rebel gathering, killing 11, military sources said.
They also attacked the rebel-held Al-Anad air base, Yemen's largest. Eight rebels and two Hadi loyalists were killed, the sources said.
UN envoy Ismail Ould Cheikh Ahmed arrived in Sanaa for talks with the rebels and their allies on his ceasefire plans.
He told reporters at the airport that he was hoping "rapidly to secure a humanitarian truce" which could pave the way for a "peaceful settlement of the crisis which has turned into a catastrophe."
On Wednesday, the United Nations declared Yemen a level three emergency, the highest on its scale.
More than 21.1 million people -- over 80 percent of Yemen's population -- are in need of aid, with 13 million facing food shortages.
More than 2,800 people have been killed in the impoverished Arabian Peninsula country since March, according to UN figures.