The Abu al-Shih company has stopped all its activities in Iraq, Ibrahim al-Zubi told Aljazeera on Wednesday.
Al-Zubi was speaking after the abduction on Tuesday of one of his drivers, Turki al-Braizat, by a group calling itself the Squads of the Unification Lions.
The hitherto unknown group announced in a videotape aired on Aljazeera that it had seized al-Braizat and would kill him within 48 hours unless his company pulled out of Iraq.
"We have returned all Jordanian trucks from the Iraqi borders to the Jordanian oil refinery," al-Zubi said.
"There have been no direct contacts between us and the captors, but we have contacted tribal shaikhs to find a solution to the problem."
He added his company was willing to meet other demands of the group if there were any.
"We have not learned the identity of the kidnappers yet, except that they are resistance," he said.
The captors claimed in the television footage that al-Braizat "admitted to ferrying fuel to the US army".
In the statement on Wednesday morning, al-Zubi admitted his truck company "transports petroleum products to the Iraqi government or the coalition forces in Iraq", although a senior company executive said on Tuesday the firm had no dealings with US troops in Iraq.
A Jordanian foreign ministry spokesman said al-Zubi signed the statement after a visit to the ministry.
"We have returned all Jordanian trucks from the Iraqi borders to the Jordanian oil refinery"
Abu al-Shih truck company owner
"We have contacted our embassy in Baghdad who are trying to make the necessary contacts to win the release of al-Breizat," the spokesman said.
"We are on top of things," he added, declining to give further details.
Al-Breizat's son, Yusuf, vowed on Tuesday to move heaven and earth to secure his father's release after learning of his capture.
"Crying and wailing over this will not help," he said, adding his father went to Iraq 10 days ago.
"I tried to call him but his mobile phone was switched off," he said.
Jordanians have been among dozens of foreigners, many of them truck drivers, seized by armed groups in Iraq seeking to put pressure on overseas employers or governments to pull out.
Ferrying fuel is big business in
Three Jordanians taken captive along with a Sudanese national were released by their captors on 6 September.
Jordan also secured the release of eight of its citizens taken in Iraq in July and August.