The temporary truce comes amid an upsurge in Saudi-led airstrikes, including one in the capital that hit the private residence of former President Ali Abdullah Saleh, said to be a rebel ally.
Saudi Arabia says the cease-fire will help get much-needed humanitarian aid into Yemen, but the offer is good only if Houthi rebels comply with the deal.
Fresh fighting around Najran comes after a nearly six-week Saudi-led air campaign against Houthi rebels. Aid agencies urge a halt to bombing Yemen's airports so humanitarian supplies can be delivered.
Saudi Arabia's King Salman shook up the monarchy on Wednesday. According to a royal decree, the king's nephew takes over as crown prince, and the king's young son becomes deputy crown prince.
Much of the world is skeptical about the wisdom of the bombing raids in Yemen. But Saudis are rallying around their new king, Salman, and his son, the defense minister.
A military spokesman said the airstrikes were giving way to a period that would include diplomatic and political efforts, alongside military operations against the Shiite Houthi rebels.