The White House is delaying approval of the export of atomic reactor components to India because it would require informing Congress of possible Indian preparations to stage a second underground nuclear test, sources said yesterday.

Because India has sunk additional shafts at its Rajasthan Desert test site, where it staged its initial atomic blast nine years ago, sources said the Reagan administration feels it would need to waive a key provision of the Nuclear Non-Proliferation Act to supply components for India's two reactors at Tarapur.

That provision, which has never been waived, requires a cutoff of U.S. atomic exports to nations the president finds are "engaged in activities involving source or special nuclear material and having direct significance for the manufacture or acquisition of nuclear explosive devices."

White House approval of such a waiver would be certain to touch off a furor in Congress. White House sources indicated it was not clear how quickly President Reagan would make a final decision.

The State Department originally hoped the decision would be made before Secretary of State George P. Shultz arrives in India for talks with Prime Minister Indira Gandhi late next week.

If the president does approve the exports, Congress would have 60 days to pass a concurrent resolution blocking the waiver. The president, however, could veto such a resolution.

While it could not be determined yesterday how recently the work at the Rajasthan Desert test site has taken place, it had to have occurred since 1980 because President Carter did not waive this provision in approving a final shipment of fuel to the Tarapur reactors.

"On the whole, we would prefer not to have to seek this kind of a waiver," an administration official said yesterday.

But to approve the atomic exports to India, the president would need to waive the provision unless steps had been taken which "represent sufficient progress toward terminating such activities" as those at the Rajasthan site, sources said.

These steps might involve filling in the test shafts, which India has not done to date, sources said.

In recent weeks, the State Department, which is eager to see India receive the parts, has been trying to line up a third country to supply the equipment to avoid the necessity of involving Congress in this issue.

Efforts have focused on Japan, Italy and West Germany.

But the State Department and the Arms Control and Disarmament Agency are recommending granting the waiver, if necessary, to provide the parts, which India says are urgently needed for safe operation of the U.S.-built reactors, sources said. The Defense Department opposes the move.

Both Reps. Richard L. Ottinger (D-N.Y.) and Edward J. Markey (D-Mass.) yesterday vowed to lead the effort to block any nuclear exports to India.

"The Reagan administration continues to make a mockery of the U.S. nonproliferation law," said Ottinger.

"I cannot believe the administration would permit trade with a nation that misused civilian technology to build a nuclear weapon in the past and apparently plans to do it again," he said.