"It is a reality check that this is happening and that Iran's oil exports will be hurt when the oil sanctions hit it in November," chief commodities analyst at Commerzbank Bjarne Schieldrop said.
"The re-imposition of U.S. sanctions on Iran remains the key (price) driver in the near-term. Supply losses could range from 600,000 to 1.5 million bpd," ANZ said on Tuesday in a note to clients.
As a result, the bank said, "the oil market should remain tight, despite OPEC increasing oil production to offset losses elsewhere."
President Donald Trump tweeted on Tuesday that the sanctions were "the most biting sanctions ever imposed," although those sanctions were originally devised and deployed by the Obama administration.
"Anyone doing business with Iran will NOT be doing business with the United States," he added.
Many European countries, China and India, oppose the sanctions, but the U.S. government said it wants as many countries as possible to stop buying Iranian oil.
"The market continues to price in geopolitical risk from the reimposition of sanctions by the U.S. on Iran," said Gene McGillian, vice president of market research at Tradition Energy in Stamford, Connecticut. "The reports that Saudi Arabia's production actually dropped in July continue to provide support for the market."
Saudi Arabia's crude production dropped about 200,000 bpd last month, two sources at the Organization of the Petroleum Exporting Countries said on Friday, despite a pledge by the Saudis and top producer Russia to raise output from July, with Saudi Arabia promising a "measurable" supply boost.
Also supporting prices were a weakened dollar, McGillian said. The dollar index was trading 0.2 percent lower. A weak dollar can lift the price of commodities, like oil, that are priced using the currency.
U.S. crude stockpiles were also expected to have dropped last week. Data from the American Petroleum Institute for U.S. inventories is due later on Tuesday at 4:30 p.m. EDT, followed by the government's report on Wednesday morning.