South Korea plans to evacuate all its civilians working in Iraq by early July, as the country waited for news about the fate of hostage Kim Sun-il.
The deadline expired at sunset on Monday
Industry Minister Lee Hee-beom said most civilians had already left, with just 22 remaining.
Islamic militants had threatened to kill Mr Kim on Monday unless South Korea ended its military role in Iraq.
A foreign ministry spokesman said on Tuesday he had "no definite answer" as to whether Mr Kim was still alive.
The South Korean government has said it is doing all it can to secure Mr Kim's release.
Seoul has also said it will go ahead with plans to deploy 3,000 troops to northern Iraq, to add to a force of 600 already in the country.
The troops are due to be involved in humanitarian and rebuilding work, and the area they are to be based in, near Kurdish-controlled Irbil, has been largely peaceful.
But the BBC's Charles Scanlon in Seoul says that internet chat sites suggest a majority of Koreans believe their troops should not be taking part in what they see as an immoral occupation.
However, the conservative press is backing the government and says it cannot surrender to terrorists.
Hundreds of South Koreans held candle lit vigils on Monday night as they waited for news about Mr Kim.
There has been no news since the expiry on Monday of a deadline set by the kidnappers, who said they would kill Mr Kim if Korean troops were not withdrawn by sunset.
Asked at a briefing on Tuesday whether the hostage was still alive, Foreign
Ministry spokesman Shin Bong-kil said: "We have various intelligence and information on that matter, but we cannot give you a definite answer".
Mr Kim's family have pleaded with the government to rethink its policy.
South Korea's Foreign Minister Ban Ki-moon has appealed for the man's release, saying South Korea is a friend of Iraq.
Mr Ban said South Korea's decision to send troops was to help in the rehabilitation of the country.
"We regard [ourselves as]... friends of the Iraqi people and there should be no cause for anyone to have kidnapped our national," he said.
In a video released by the militants on Sunday, which was broadcast on Arabic TV channel al-Jazeera, Mr Kim was seen screaming: "Korean soldiers, please get out of here. I don't want to die. My life is important."
The two-minute video showed the hostage surrounded by armed men wearing masks.
The tape said that the 24-hour deadline would expire at sunset (2015 local time, 1615 GMT) on Monday and that after that the Korean would be executed.
A banner identified the group as Jamaat al-Tawhid and Jihad, which is led by a leading al-Qaeda member, Abu Musab al-Zarqawi.
Last month, the same group beheaded an American hostage, Nick Berg, and it has been responsible for a number of other attacks, including the killing of Iraqi Governing Council head Ezzedine Salim.