The clashes broke out in a northwestern district of the capital Sanaa near a state TV building, when troops stopped a rebel truck loaded with weapons, military officials said, adding that there were no casualties. They spoke on condition of anonymity because they were not authorised to speak to the press.
The flare-up came as the Shiite rebel group, known as the Hawthis, was said to have been close to signing a deal reached through an international mediator.
The crisis was sparked by the government's decision to slash the subsidies in late July as part of an austerity plan. Yemen is one of the poorest countries in the Arab world.
The officials said the Hawthis insist on signing the deal in their stronghold in the northern city of Saada, while the president wants to sign it in the capital.
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Yemen's top Western allies issued a joint statement expressing grave concern about the "rising threat to the security of Yemen" and urged the Hawthis "to negotiate in good faith with the government of Yemen to resolve political grievances and differences."
The Hawthis control the northern province of Saada and have a strong presence in cities near the Saudi border. Yemen is also grappling with strong al-Qaida affiliate that mainly operates in the south and east, as well as an increasingly assertive southern separatist movement.
The United States has long provided aid to Yemen's counter-terrorism forces and regularly carries out drone strikes aimed at al-Qaida militants.