None of those countries is part of the 160,000-member force in Iraq, however Iraqi resistance factions view companies working with the US-led occupation in Iraq as collaborators.
"We announce we have captured two Kenyans, three Indians and one Egyptian. We tell the company to withdraw and close its offices in Iraq," said one of the masked men, from a group
calling itself the "Black Banners".
The deadline starts from 8 pm (local time) on Wednesday, it said.
The captors in a statement also demanded that India, Kenya and Egypt withdraw their citizens from Iraq. None of the three countries are part of the US-led military force in Iraq but many of their nationals work as drivers and contractors.
Interim Prime Minister Iyad Allawi appealed last week to India and Egypt to send troops.
"We have warned all the countries, companies, businessmen and truck drivers that those who deal with American cowboy occupiers will be targeted by the fires of the Mujahideen," the statement said. "Here you are once again transporting, goods, weapons and military equipment that backs the US Army."
The statement came a day after Filipino hostage Angelo de la Cruz was released after his country gave in to their demand and pulled its 51-member force out of Iraq.
Filipino captive De la Cruz was
freed after demands were met
More than 60 foreigners have been taken captive in Iraq in recent months.
In photos provided to AP with the statement, six of the hostages are shown standing behind three seated, masked armed men.
One of the hostages holds a paper with the typed names of seven men their nationalities, passport numbers and the registration numbers of the trucks they were driving.
Names of captives
The paper is stamped 20 July and the words "Universal Services" were handwritten on top.
The names on the paper were Ibrahim Khamis, from Kenya, Salm Faiz Khamis, from Kenya, Jalal Awadh, from Kenya, Antaryami, from India, Tilak Raj, from India, Sukdev Singh, from India, and Muhammad Ali Sanad, from Egypt.
It was not clear which of the Kenyans listed on the paper was not among the group.
"They will chop off our heads"
Muhammad Ali Sanad,
In a video broadcast on the Arab satellite television station Al-Arabiya, one of the hostages, an Egyptian citizen who identified himself as Muhammad Ali Sanad, called on the company to pull its employees from Iraq to save his and the others' lives.
"They will chop off our heads," he said. "Who will feed my family, my brothers and sisters? I urge the company to work to send us to our countries," he said.
From the statement, the trucking company that employed the men appeared to be based in Kuwait and the captors warned that every Kuwaiti company dealing with Americans "will be dealt with as an American."