Marib is vital because it is the internationally recognised government's last stronghold in North Yemen, and the country's sole gas producing region with one of its largest oilfields.
Rebels target northern city with a ballistic missile, killing two government soldiers and three civilians, a local medic says.
Fighting also raged between Yemen's government forces and the Houthis elsewhere including in the provinces of Jawf and Taiz, military officials say.
Abu Dhabi-trained Giants Brigade fighters say "hundreds were killed and wounded on both sides" before Houthi rebels were allegedly expelled from a key district south of energy-producing Marib region.
The push for energy-rich Shabwa came amid heavy air strikes by the Saudi-led coalition battling the Houthi rebels elsewhere in Yemen, including the capital Sanaa.
The friendly fire incident follows an escalation in fighting between the Houthis and Yemeni government forces around the central city of Marib.
At least four soldiers were killed and 13 others wounded at the camp in the southern province of Shabwa.
Government forces advanced a few kilometres following fierce battles south of the city, one of the officials said.
Over 45,000 people are fleeing their homes as Houthi forces push to usurp Marib, the city that has seen around 1 million people flee since late 2014.
Over 150,000 people will be killed in fighting alone in Yemen this year, the UN agency says while an estimated 1.3 million people in total will have died by 2030.
The Houthis have detained Yemeni staff in the US compound in a daring attack, which might be a message to Washington that they are in charge in the capital.
Coalition operations took place in Sirwah to the east of Marib city and Al Bayda province to the south.
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