The men, said to be three Albanians and a German, were captured in southern Afghanistan, a Taliban spokesman said.
Mullah Omar's order was read by telephone late on Sunday to a Reuters reporter at the border town of Spin Boldak, in Kandahar province.
Qari Mohammad Yousuf, a Taliban spokesman, quoted the order as saying: "These people had come to Afghanistan at America's behest, therefore they should be sentenced to death."
Earlier on Sunday, Yousuf had said four Albanians and four Afghans were being held.
But he later said the four Afghans, two of them drivers, had been released, and identified the foreigners as three Albanians and a German.
The Afghan authorities could not say what the kidnap victims had been doing in Kandahar province.
A Taliban court would try the men as spies for the United States, Yousuf said.
In the past, the Taliban has kidnapped employees of companies and non-government organisations involved in Afghanistan's reconstruction and accused them of spying.
The authorities in Kandahar said a search was on for the men, who had been travelling in two vehicles when they were held up at gunpoint.
US-led forces overthrew the Taliban government in late 2001, after its leadership refused to surrender Osama bin Laden after the attacks on the US on 11 September that year.
Since then, the Taliban has been fighting to overthrow the US-backed government of Hamid Karzai, the president, and to force out foreign troops.
The insurgents have killed several foreigners after kidnapping them, including a Briton involved in a road project who was found dead in September and an Indian killed in November.
Both men were killed within days of their abduction.