The United States is pushing foreign countries to cut their oil imports from Iran to zero by November, a senior State Department official said Tuesday, as the Trump administration escalates its bid to pressure Iran after pulling out of the nuclear deal.

The price of U.S. crude jumped to more than $70 per barrel for the first time since May on the news that countries were expected to completely eliminate their imports, rather than making a "significant" reduction. The Trump administration does not intend to give out waivers allowing countries such as close allies to keep importing, the official said.

The official wasn't authorized to be identified by name and briefed reporters on condition of anonymity.

Last month, President Donald Trump announced the U.S. was leaving the 2015 deal, in which sanctions on Iran — including its energy sector — were eased in exchange for Tehran agreeing to roll back its nuclear program. His administration said the oil sanctions would be going back into effect after a six-month grace period that expires Nov. 4.

At the time, the Treasury Department had issued public guidance suggesting that countries needed to make a "significant reduction" in their imports, or else they would be subject to separate U.S. sanctions prohibiting all transactions between their central banks and Iran's central bank.

But the official said that Trump administration officials have been visiting European and Asian countries to say that the U.S. expects their imports to be zeroed out by the time the grace period ends.

The official also said the U.S. is working with other Middle East countries to increase production so the global oil supply isn't harmed.

Some close U.S. allies are among the largest imports of Iranian crude oil, including India and South Korea. Japan and Turkey also import significant amounts of Iranian oil, according to statistics from the U.S. Energy Information Agency. The biggest importer of Iranian oil last year was China, which has remained a party to the Iran nuclear deal despite the U.S. withdrawal.