"We were kidnapped in Baghdad at around 8.30am on Sunday as we were being taken to work in a minibus," Ahmad Swaif, 23, told AFP on Tuesday.
Swaif was speaking from the Egyptian embassy in Baghdad along with a freed colleague, Muhammad al-Saaidi, 25, both of whom are from Cairo.
The four were "stopped by masked men somewhere in Baghdad. I can't say exactly where because I don't know the city very well," said Swaif.
The engineers were taken to a house where the kidnappers asked just one question: "Who do you work for?"
"We answered that we work for Orascom, building communication towers, and they said that they would make inquiries about our relations with the Americans. They treated us well," said Swaif.
The Egyptians work for the Egyptian-Iraqi company Servco, a subcontractor for Orascom, an Egyptian company that runs central Iraq's mobile network.
However, there were contradictory versions of the men's release.
Swaif said that on Monday evening "they let us go in the street and after around 10 minutes we came across security forces who took us to the Egyptian embassy." He declined to say whether the forces were American or Iraqi.
Orascom chairman Naguib Sawairis told CNN that two of the four had been freed by US and Iraqi forces in a joint operation while the other two had escaped. He said one kidnapper was arrested.
"The kidnappers put them in the trunk of the car and they (the two) managed to break through this car and run away. They were shot at but they managed to come to our offices," Sawairis said.
He added that the company had received a half-million-dollar ransom demand, but did not respond.
Orascom's mobile phone network in the Baghdad area, Iraqna, has been repeatedly accused by the government of helping the resistance and by the resistance groups of assisting the US military. In September, 10 of its employees were captured but later released.
"All four of us are going to have a holiday in Egypt, and we will then come back to Iraq to continue our work," said Swaif. His colleague nodded his agreement.