WASHINGTON — The Trump administration has reached a critical juncture in its efforts to tighten United States oil sanctions against Iran and Venezuela.

By pressuring China and India to end or sharply reduce oil purchases from Iran and Venezuela, American officials are seeking to cut off a key economic lifeline for what the administration considers to be two rogue nations that threaten the stability of the Middle East and Latin America.

But they must do that without roiling global markets, further straining relations with China and India or raising gasoline prices in the United States.

The dilemma has led to a fierce debate within the Trump administration, which is set to decide by May 2 whether to extend waivers allowing China, India and three other nations to buy Iranian oil. A halt of oil shipments would constrict global oil supplies and increase costs at a time when much of the world economy is slowing.