The Kuwait and Gulf Link Transport Company said in a statement on Sunday that it was negotiating with the Black Banners group through some "Iraqi friends".
"There are promises and assurances the hostages will be freed, especially after the kidnappers became certain that we have no presence in Iraq and we were just conducting transportation for the interest of some Iraqis," the firm said.
The Iraqi captors meanwhile are reported to have appointed a senior tribal leader Shaikh Hisham al-Dulaymi to negotiate the release of the three Kenyans, three Indians and an Egyptian.
Indian Foreign Minister Natwar Singh also appealed for the release of the captives on a day that witnessed more bloodshed in Iraq.
Up to 13 Iraqis were reported killed in fighting between US occupation forces and resistance fighters north of Baghdad.
Singh said India refuses to send troops to Iraq out of respect for Iraq's solidarity and the feelings of the Iraqi people.
Dozens of foreigners have been seized in Iraq since April. Some have been freed but at least six have been killed by their captors, four of them by beheading.
Meanwhile, the daughter of a Pakistani national feared captured made an emotional appeal for his release.
"I miss my father very much. I urge the Pakistani government and Iraqi people to help find my father," said Nazia, appealing for the release of Raja Khan.
The two Pakistanis, an engineer and a driver working for the Kuwait-based al-Tamimi company, disappeared on Friday.