Coupled with a Saudi-led blockade and internal clashes, the stalemate has contributed to a human catastrophe threatening some 7 million people with famine.
Fighting and air strikes have intensified in the Yemeni capital of Sanaa following the death of former president Ali Abdullah Saleh. Roads are blocked and tanks are deployed on many streets, trapping civilians and halting delivery of vital aid including fuel to supply clean water, the United Nations (UN) said on Monday.
Some of the fiercest clashes are around the diplomatic area near the UN compound, while aid flights in and out of Sanaa airport have been suspended, the world body said in a statement following its appeal for a humanitarian pause on Tuesday.
"The escalating situation threatens to push the barely functioning basic services ... to a standstill. These services have already been seriously compromised with the latest shock of the impact of the blockade," it said, adding that fighting had also spread to other governorates, such as Hajjah.
For two years the war has been one of attrition along mostly static front lines.
Coupled with a Saudi-led blockade and internal clashes, the stalemate has contributed to a human catastrophe. Some 7 million people are on the brink of famine, while one million are suspected to be infected with cholera.
Eyes will now turn to Saleh's political allies and military commanders, whom analysts credited with aiding the Houthi march southwards in 2014 to dominate swathes of western Yemen.
Adam Baron, a Yemen expert at the European Council on Foreign Relations, said it was not yet clear what Saleh's family and political allies would do.
"His people will be angry, and many will certainly be out for blood, but there are many in the middle, especially among the tribes, who will fall in with whoever appears stronger," he said.
"The (Saudi-led) coalition may have put a lot of their eggs in Saleh's basket, only for it to fall over now. They appeared to strongly support his attempt to confront the Houthis, and now that bid may have failed."