"I am ceasing operations and pulling out from the company's premises in Iraq for humanitarian reasons, and out of my concern for the safety and the lives of my two employees who were kidnapped in Iraq," Rami al-Uwais told said on Tuesday.
Fayiz Saad al-Udwan and Muhammad Ahmad Salama Almanaya, who work as drivers for the private company Daud and Partners, were captured on Monday by an Iraqi group calling itself the Mujahidin Corps in Iraq.
"I am ceasing operations and pulling out from the company's premises in Iraq for the safety and the lives of my two employees"
Daud and Partners chief executive
The group warned they would be killed within 72 hours unless their employer withdrew from Iraq and stopped cooperating with US forces there.
"Like other Jordanians, I have always been supportive of our brothers in Iraq and in all circumstances," chief executive al-Uwais said in his withdrawal statement.
He declined to say when the firm would leave Iraq, but indicated it was in the process of doing so.
The wife of al-Udwan, Umm Muhammad, promptly thanked al-Uwais for his "wise decision".
"We hope it will lead to my husband's release and safe return home," she said.
Earlier on Tuesday, relatives of the captives had threatened to behead al-Uwais and kill all the company's staff unless the firm did not immediately comply with the captors' demand to cease operations in Iraq.
"We told the firm's executive director, Rami al-Uwaiss, that if he does not comply with the kidnappers' demands today, his company and the lives of his employees will not be spared," said al-Udwan's brother, Umar.
Al-Manaya's father, Ahmad Salama, said: "We will chop off the head of the firm's director if he doesn't heed our demands to completely cease his operation in Iraq."
Both men spoke to reporters at a gathering of relatives of the two men outside the Amman offices of Daud and Partners in Jordan.
Representatives of both their families held a 40-minute meeting with senior company staff on Tuesday.
The company provides construction and catering services to the US military in Iraq.