Senior administration officials now agree that China defied US sanctions when it imported more than a million barrels of crude oil from Iran last month. But they are grappling with whether – and how – to hit back, according to three US officials.

The US State Department had considered issuing a waiver allowing Chinese companies to receive Iranian oil as payment in kind for their investment in an Iranian oilfield, but that idea has been abandoned.

China hawks on the National Security Council are now pushing for the US to impose secondary sanctions on Chinese entities, a move that would complicate trade talks between the two countries and further strain the relationship.

The Trump administration has been pushing to reduce Iran’s oil exports to zero as part of its policy of “maximum pressure” on Tehran amid the worsening stand-off over Iran’s nuclear programme. It has had some success in persuading several of Iran’s largest consumers – India, Japan, South Korea and Turkey – to curb their purchases.

But Beijing is a tougher customer. In June, a tanker carrying up to a million barrels of Iranian oil docked near the Chinese port city of Qingdao, drawing complaints from Republican lawmakers, who demanded the Trump administration pressure China to stop.

China has also reportedly welcomed a second batch of Iranian oil since its previous waiver expired in May – this one a two-million barrel shipment that docked in Tianjin.

China’s continuing defiance would seem to undercut the Trump administration’s claim that its efforts to squeeze Iran are working. In a recent speech, national security adviser John Bolton announced that “all significant reduction exceptions on Iranian oil sales have gone to zero”.

The internal dispute over how best to pressure Beijing comes as Iran declares it has enriched uranium behind the limits proscribed in its July 2015 agreement with major world powers, including the United States.

The announcement has set off a flurry of diplomatic activity, with European countries scrambling in recent days to convince Iran to return to the deal’s constraints, and US President Donald Trump warning Iran to “be careful”.

The United States withdrew last year from the nuclear deal with Iran, formally known as the Joint Comprehensive Plan of Action, but has yet to find a diplomatic path forward as tensions increase. Trump ordered military strikes after Iran shot down a US drone, only to call it off at the last minute.

The administration has demanded that Iran comply with the terms of the JCPOA, even though Trump has repeatedly slammed it as “the worst deal in history”. His aides, meanwhile, have struggled to explain how they intend to compel or induce Iran to engage in negotiations for a deal to replace it – beyond adding still more pressure.

At an emergency meeting of the International Atomic Energy Agency in Vienna on Wednesday, which ended inconclusively, US officials accused Iran of “nuclear extortion” and threatened to impose a new round of sanctions.

“The special meeting of the Board of Governors ended without any results for America,” boasted Kazem Gharibabadi, Iran’s ambassador to the IAEA, following the meeting.

Late on Wednesday, Trump said in a tweet that “[s]anctions will soon be increased, substantially” – but did not specify what Iran might need to do to avoid that fate.

Nor is it clear what the administration would consider acceptable concessions on Iran’s part.

Secretary of State Mike Pompeo has outlined 12 conditions Tehran must meet as part of any US-Iran talks, but many Iran analysts consider them politically impossible for Iranian leaders to accept – and Trump has at times brushed them aside, offering to talk with Iranian leaders without preconditions.

Iran’s supreme leader, Ayatollah Ali Khamenei, has likened the idea to “drinking poison.”

Meanwhile, the US is vowing to keep tightening the screws on Iran.

In his July 7 speech, Bolton said: “We will continue to increase the pressure on the Iranian regime until it abandons its nuclear weapons programmes, and ends its violent activities across the Middle East, including conducting and supporting terrorism around the world.”