The pipeline had been designed to link a vast gas field in eastern Turkmenistan to Pakistan through Afghan territory - one of the most ambitious schemes to unlock central Asia's energy reserves for the Asian and Western markets.
The BBC Central Asia correspondent says the news will come as a severe blow to Turkmenistan, which is desperate to get its huge gas reserves out to market.
A Unocal spokeswoman said the company had no plans to cancel the project but she admitted it was far from clear when it would start again.
The company will be meeting with its six foreign partners to discuss the situation.
Ever since a consortium to build the pipeline was set up 10 months ago, it struggled to achieve funding targets, hampered by the internal conflict and instability that has continued to plague Afghanistan.
The major problem was that with no internationally recognised government in power in Afghanistan, no external financing could be forthcoming.
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