The general manager of Sanaa International Airport, Naji al-Murqab, told the defence ministry's news website 26sep.net that airlines were informed "all problems and obstacles which were threatening planes" had been resolved.
An official at the airport from Yemenia Airways said three international flights took off on Sunday headed for Beirut, Cairo and Dubai, while several domestic flights took off and landed.
Civil aviation chief Hamid Faraj also confirmed to state news agency Saba, which resumed online services after its website had been hacked and brought down for two days, that flights were back to normal on Sunday.
The "airport was shut down due to threats the control room has received from armed groups... who opened fire in areas near the arrival and departures tracks," he said.
A military source said on Saturday that Ahmar had refused to comply with President Abdrabuh Mansur Hadi's order to go unless the defence minister and other senior officials also stepped down.
He also demanded that several members of the powerful Hashed tribe, which backed defectors during last year's anti-Saleh protests, be forced into exile.
An air force official told AFP later on Sunday that Ahmar left the air force headquarters on Sunday but could not say if he had agreed to step down.
Political sources in Sanaa said Ahmar had come under pressure from several parties, including Western ambassadors in Sanaa, to retract a decision to obstruct air traffic.
On Saturday, an airport official said the facility was closed after forces loyal to Ahmar had threatened to shoot down planes.
But a military official said the decision came after an air force officer had fired 10 shots at the control tower demanding compensation for land belonging to his tribe that was seized to expand the airport.
In addition to Ahmar, Hadi also sacked Saleh's nephew, General Tareq Mohammed Abdullah Saleh, who heads the presidential guard.
At the same time, Hadi fired General Mohammed Ali Mohsen al-Ahmar, leader of units in the eastern region who is loyal to General Ali Mohsen al-Ahmar, together with whom he defected to the opposition last year.
The moves were hailed by the United States, which has long made Yemen a major focus of its "war on terror," as well as by the the six-nation Gulf Cooperation Council (GCC) states.
"The United States welcomes President Abdrabuh Mansur Hadi's announcement of civilian and military personnel transfers as part of the ongoing political transition in Yemen," US State Department acting spokesman Mark Toner said.
"In spite of those who seek to derail the transition, President Hadi has demonstrated strong leadership by steadfastly implementing the agreed-upon political settlement," Toner added.
GCC chief Abdullatif al-Zayani, who led mediation efforts to convince Saleh to step down, also said the grouping "supports" Hadi and "backs all measures he takes to help Yemen exit its current crisis."
In other developments, the defence ministry and a tribal chief said on Sunday that air strikes had killed 24 Al-Qaeda suspects in their strongholds in the south and east.
A Yemeni air raid late on Saturday killed 16 extremists near Zinjibar, 26sep.net reported, while a tribal chief said a US drone in the eastern province of Shabwa left eight militants dead.
Hadi, who is restructuring the army based on the Gulf-brokered deal that ended Saleh's 33 years in power, also faces the challenge of a growing Al-Qaeda threat since he took office in February.