Houthi rebel artillery pounded residential areas near the city of Taiz, witnesses said.
However, the capital Sanaa and central Yemen are understood to be quiet.
Before the truce was due to begin, clashes were reported at a major air base north of Aden after government allies took the  nearby town of Sabr.
The Saudi-led coalition said it would halt air raids at midnight (20:59 GMT) to let much-needed humanitarian aid in.
But a Houthi spokesman said the rebels would not adopt a position on the move until they were officially informed.
Earlier reports suggested that the Houthi leader, Abdel-Malek al-Houthi, had pledged to continue the fight.
A correspondent with AFP news agency also reported sporadic gunfire in the northern outskirts of Aden barely an hour after the unilateral truce came into force. Rebels there are trying to halt the advance of loyalist forces who have retaken the port city.
On Saturday, the coalition said it would suspend bombardment for five days but that it reserved the right to respond to "military activity or movement" by Houthi rebels.
The unexpected ceasefire was announced after Yemen's President Abdrabbuh Mansour Hadi wrote to Saudi's King Salman asking for a break, to allow humanitarian supplies to be delivered.
It came after strikes in Taiz province, which reportedly killed 120 people, including civilians.
Aid agencies say a blockade on Yemen has worsened the humanitarian crisis which is gripping the country.
More than 80% of Yemen's 25 million people now need some form of aid.
The Saudi-led coalition has been bombing Houthi militia and forces loyal to former president Ali Abdullah Saleh since 26 March.
The UN has warned the coalition that indiscriminate bombing of populated areas is against international law.
A week-long truce brokered by the UN failed earlier this month.
At least 1,693 civilians have been killed in fighting in Yemen, with almost 4,000 people wounded. The UN said the majority of casualties were caused by air strikes.
Houthis - The Zaidi Shia Muslim rebels from the north overran Sanaa last year and then expanded their control. They want to replace Mr Hadi, whose government they say is corrupt. The US alleges Iran is providing military assistance to the rebels.
Ali Abdullah Saleh - Military units loyal to the former president - forced to hand over power in 2011 after mass protests - are fighting alongside the Houthis.
Abdrabbuh Mansour Hadi - The president fled abroad in March as the rebels advanced on Aden, where he had taken refuge in February. Loyal soldiers, Sunni Muslim tribesmen and Southern separatists have formed militia to fight the rebels.
Saudi-led coalition - A US-backed coalition of nine, mostly Sunni Arab states says it is seeking to "defend the legitimate government" of Mr Hadi.
Al-Qaeda in the Arabian Peninsula - AQAP opposes both the Houthis and President Hadi. A rival affiliate of Islamic State has also recently emerged.
Frontline voices from Yemen conflict
Failure 'not an option for Saudis'
Meeting the Houthis - and their enemies
Shelling has been reported in southern Yemen just as a humanitarian truce between rebels and Saudi-backed pro-government forces came into force.