The U.S. will impose sanctions on some Chinese entities for knowingly transporting oil from Iran, Secretary of State Mike Pompeo said, the latest attempt from Washington to ratchet up pressure on Iran.

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"The more Iran lashes out, the greater our pressure will be," Pompeo said Wednesday morning, during a speech on the sidelines of the United Nations General Assembly.

The Trump administration ordered a fresh round of sanctions against Tehran last week, in response to an earlier attack on Saudi Arabia's oil production facilities. Those sanctions targeted Iran's central bank, which Treasury Secretary Steven Mnuchin said was the nation's last source of funds.

“This is very big,” Mnuchin said at the time. “We’ve now cut off all source of funds to Iran.”

Although Yemen's Houthi rebels initially claimed responsibility for the attack -- which resulted temporarily in a loss of roughly 6 percent of the world's oil output -- the U.S. and its European allies suspect Iran was behind the attack.

Iran denies the accusations.

Pompeo also said the U.S. will take steps to disentangle the Islamic Revolutionary Guard Corps from the Iranian economy by educating countries about the risk of doing business with IRGC entities.

"We will punish them if they persist in defiance of our warnings," he said.

Pompeo's announcement came one day after Trump's speech before the UN General Assembly, during which he condemned Iranian leaders' "bloodlust" in a scathing speech.

“All nations have a duty to act. No responsible government should subsidize Iran’s bloodlust. As long as Iran’s menacing behavior continues, sanctions will not be lifted, they will be tightened,” Trump said.

Iran has refused to negotiate with the U.S. unless it returns to the 2015 Iran nuclear deal, which Trump abandoned last year.

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