The United States' inability to foresee or forestall India's nuclear tests, despite ample warnings, was a failure of both the Central Intelligence Agency and American foreign policymakers, Government officials said today.

After the chairman of the Senate intelligence committee called it ''the intelligence failure of the decade,'' the Director of Central Intelligence, George J. Tenet, asked retired Adm. David E. Jeremiah, a former Vice Chairman of the Joint Chiefs of Staff, to lead a 10-day investigation into the intelligence community's failure to detect preparations at the test site in the Indian desert.

The site has been under periodic surveillance by photo reconnaissance and electronic eavesdropping satellites, which recorded increasing activity. But the images and activities they recorded in recent days were not interpreted clearly or quickly by the C.I.A., officials said.

That oversight constituted ''a colossal failure on the part of our intelligence agencies,'' said the chairman, Richard C. Shelby, Republican of Alabama. ''Something went wrong. Somebody failed to do their job. To let this slip up on our policy makers, the President, the Secretary of State, without a chance to intervene in some way diplomatically with India was a huge intelligence failure. If we had an inkling that they were going to detonate one or more nuclear weapons, perhaps we could have intervened. We certainly would have tried.''