WASHINGTON — The Trump administration is softening its earlier demand that countries like China, India and Turkey end all imports of Iranian oil by Nov. 4, as a top State Department official on Monday said the United States would allow reduced oil flows, in certain cases.

“We are prepared to work with countries that are reducing their imports on a case-by-case basis,” said Brian Hook, the department’s director of policy and planning.

His announcement was a delicate attempt at reassuring oil markets and allies that sanctions are not likely to hit them this fall — even if Iranian oil continues to flow around the world, as is likely the case.

India, South Korea and Turkey — all allies or friends of the United States — are major importers of oil from Iran and are unlikely to be able to switch suppliers entirely by November.