"This decision is intended to bring Iran's oil exports to zero, denying the regime its principal source of revenue," she said.
Secretary of State Mike Pompeo later told reporters the countries that did not abide by the embargo will face sanctions. "Any nation or entity interacting with Iran should do its due diligence and err in the side of caution," he said.
In New Delhi, Indian sources said "We have seen the announcement by the US Secretary of State. We are studying the implications of the decision and will make a statement at an appropriate time."
Ending the waiver is a disappointment for India, which had hoped for an extension of the exemption beyond May 2. Foreign Secretary Vijay Gokhale had discussed extending the waivers when he met US officials in Washington last month for the India-US Strategic Dialogue.
When the US tightened sanctions on Iran in November, India and seven other countries were given the exemptions, enabling them to continue buying oil.
Asked if there would be a wind-down period for the countries to complete pending transactions after the waiver ends next week, neither Pompeo nor other US officials addressed it directly only repeating the waivers end on May 2.
To soften the impact on countries that lose waivers, he said "We stand by our allies and partners as they transition away from Iranian crude to other alternatives."
The US is increasing oil production and working with Saudi Arabia and the United Arab Emirates (UAE) to ensure that there is no oil supply disruptions due to end of the waivers, he said.
However, oil prices surged with first indications on Sunday night that waivers would end. Brent crude, which serves as the benchmark for oil prices, surged more than 2.5 per cent to nearly USD74 per barrel -- the highest in about six months -- on Monday.
India was reportedly importing about 1.25 million tonnes of oil per month from Iran, about half of what it had been importing before the restrictions. Nearly 10 per cent of the 220 million tonnes crude oil India imported in 2017-18 came from Iran.
In May last year, Trump withdrew from the 2105 international agreement with Iran on de-nuclearisation that had ended sanctions on that country. When Trump re-imposed tough sanctions on Iran in November, he gave six-month temporary waivers to continue buying oil to China, Japan, South Korea, Taiwan, Turkey, Italy and Greece too.
India's vulnerability to US sanctions if it decides to continue buying Iranian oil will be through curbs on banks and oil tankers.
Although China reportedly has put oil imports from Iran on hold, it forthrightly criticised the US.
Foreign Ministry spokesperson Geng Shuang told reporters in Beijing "China opposes the unilateral sanctions and so-called 'long-arm jurisdictions' imposed by the US. Our cooperation with Iran is open, transparent, lawful and legitimate, thus it should be respected."
(Arul Louis can be reached at email@example.com and followed on Twitter @arulouis)