Al-Alimi, who chairs the country's Presidential Leadership Council, said in a televised address the objective is to "restore state institutions and extend sovereignty over the entire national territory," all the way to the Yemeni capital Sanaa being controlled by the rebel Houthi militia.
Al-Alimi also announced safe return with amnesty for anyone who abandons the Houthi movement and stops fighting in their ranks.
The call to arms was directed both at residents within Yemen and those abroad, including tens of thousands of refugees who fled after the war broke out in 2014.
The decade-long conflict between government forces and Houthi rebels has displaced an estimated five million people.
Al-Alimi addressed residents of the Houthi-controlled areas, urging them to protect their children's lives and not to send them to fight along the Houthi militants.
"The state does not view you as a party to a conflict, but rather as its people and its partners," he said.
The Iran-aligned Houthi rebels have been fighting Yemen's Saudi-backed government for more than a decade.
A 2022 truce left the conflict largely frozen, but also with little prospect of an end to the war.
In recent weeks, the Houthi rebels have intensified their missile and drone attacks on neighbouring Saudi Arabia, and imposed a blockade on its vessels, accusing the kingdom of besieging the Yemeni areas under the militia's control.
The Houthis earlier this month seized the western coast of Yemen in a lightning offensive, gaining access to the strategically important Bab el-Mandeb Strait.
The swift Houthi advances raised questions about the effectiveness of the Saudi-backed forces in the face of the disciplined and well-armed Houthi fighters.
Al-Alimi's speech came on the 64th anniversary of a military coup that ousted the monarchy ruling northern Yemen, rooted in the Zaydi Shi'Ite sect to which the Houthis also belong.
The Houthis battled Yemen's central government for years before sweeping down from their northern stronghold and seizing Sanaa.
with AP and EFE
