The fighting and air raids in Mukayris, a town seen as a gateway to southern provinces recently recaptured by pro-government forces, left 19 rebels, 15 loyalists and six civilians dead, the sources said.
Coalition strikes against rebel positions in Baida continued today as fighting raged on, the sources added.
Baida is home to mainly-Sunni tribes who have been fighting Shiite Huthi rebels since the militia advanced from its northern stronghold late last year.
Other clashes were ongoing today and coalition raids struck rebels in the vast oil-rich Marib province, in the east, witnesses said.
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Yesterday, one local official said that up to 53 Huthis were killed in coalition air strikes on Marib.
But there was no independent confirmation of the report.
The Huthis have seized control of large parts of the country including Sanaa, forcing President Abedrabbo Mansour Hadi to flee to the southern port city of Aden and then Saudi Arabia.
The kingdom, as well as the United Arab Emirates, have also backed pro-government forces with arms and troops.
Riyadh accuses Tehran of arming the Huthis, a charge it denies.
The latest fighting had been focused in provinces surrounding Sanaa, including third-city Taez -- seen as key to controlling the capital.
Residents reported that Taez was quiet early today following a night of clashes and air strikes.