Yemeni officials continue to accuse the Houthis of violating the terms of the cease-fire, which both sides signed in February after six months of brutal fighting. The truce required the Houthis to implement six conditions, including the removal of roadblocks in northern Yemen and the release of prisoners.
"Despite the halting of military operations... and the Houthis committing to the truce, they have been avoiding the full implementation of the six terms," an unnamed official told Yemeni state media earlier this week.
The Houthis, meanwhile, issued a statement on Monday that accused the government of a military build-up in Saada province, where much of the fighting took place.
"The continuation of reinforcements to Saada after the sixth round reflects the aggressive intentions of the authority," the rebels said in a statement.
"We want peace and stability; however, the reinforcements force everyone to carefully rethink the possibility of a new war at all levels."
Saleh tried to dial down those tensions on Tuesday at a news conference in Sanaa, the capital.
"There are no indicators for a seventh war," Saleh said.
The Houthis have fought six wars with the government since 2004. They blame the central government for economic and religious discrimination. Previous cease-fire agreements have typically collapsed after a matter of months.
The United Nations estimates that nearly 300,000 people have fled their homes during the six years of fighting. Few of them have returned since the cease-fire.