The Saudi-led coalition, which launched an air war against Huthi Shiite rebels and their allies in March, said the truce began as scheduled at midday (0900 GMT).
But just hours later, rebel artillery and tanks killed seven civilians and wounded 15 in residential areas of the southwester city of Taez, witnesses and medics said.
Two loyalists had already been killed in the east and mortar rounds hit government forces in Taez province after the truce took effect, officials said.
The violations came even after rebel military spokesman General Sharaf Luqman "welcomed" the call for a ceasefire, in a statement on the sabanews.Net website.
He said he hoped "aggressor parties would truly and seriously commit to a halt in fighting".
A spokesman for rebel-allied ex-president Ali Abdullah Saleh's General People's Congress, which is represented in Switzerland, made a similar statement.
He urged "all parties to commit to a complete and permanent ceasefire", in a statement on the party's almotamar.Net website.
Previous UN efforts have failed to narrow differences, with ceasefire attempts foiled.
He said the peace talks "seek to establish a permanent ceasefire and pave the way for a return to a peaceful and orderly political transition".
But Farea al-Muslimi, a Yemen expert at the Carnegie Middle East Center, was pessimistic.
"Even if you had no Al-Qaeda and... No (Islamic State group), there are already too many stakeholders in this war," he told journalists in Washington.
"There is a complete absence of political legitimacy in Yemen right now; everyone is fighting everyone."
Before the truce, clashes shook Taez and coalition warplanes bombed rebel positions.
Saba news agency later quoted local activists as saying rebels carried out "dozens of violations of the ceasefire" there since midday.
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