The latest fighting comes despite an ongoing ceasefire and UN-brokered peace talks in Kuwait that began in April.
Battles raged in Bayhan, on the border between Shabwa province in the south and Marib in the east.
There was also fighting in Sarwah, an oil-rich area west of Marib, the sources said.
At least 23 rebels and 15 soldiers were killed in both areas, the same sources said.
Bayhan is the only part of Shabwa province still controlled by the Iran-backed rebels, who on Tuesday retook positions seized by loyalists during the past two days, the military sources said.
Meanwhile, media rights watchdog Reporters Without Borders (RSF) said that "sniper fire" from the Huthi rebels killed Yemeni journalist Abdullah Azizan while he was covering the clashes in Bayhan on Sunday.
Azizan worked for the local marebpress.Net news website.
Forces loyal to President Abedrabbo Mansour Hadi are backed by a Saudi-led coalition that began a military campaign against the rebels in March 2015.
Loyalists, backed by coalition firepower, managed to drive rebels out of Shabwa and four other southern provinces last summer.
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