Front-month Brent crude oil futures were at $72.87 per barrel at 0111 GMT, up 26 cents, or 0.4 percent, from their last close. French energy giant Total has already said it is pulling out of its multi-billion-dollar investment project in the South Pars oil field in southern Iran as a result of the renewed sanctions. USA light crude was unchanged at $67.63 a barrel.
Fears that the escalating tensions could lead to a slowdown in global economic growth and a corresponding hit to demand for oil have weighed on crude prices in recent weeks.
The trade dispute is also boosting the US dollar against emerging-market currencies, and oil consumers in those countries pay more for oil in their local currencies, another potential risk to demand growth.
That is compounding worries that a deepening trade war between the United States, China and the European Union will squeeze business activity in the world's biggest economies.
At the same time, OPEC lowered its global oil-demand growth estimate by 20,000 bpd, to 1.64 million bpd this year.
The United States will seek to block Iran's worldwide oil sales from November 5, when the second phase of sanctions are reimposed as part of Washington's withdrawal from the 2015 nuclear deal.
Erdogan says Turkey to 'boycott' USA electronic goods
After free-falling on Monday , Turkey's already troubled lira began showing signs of stabilizing on Tuesday, climbing 5 percent. Turkish Foreign Minister Mevlut Cavusoglu told reporters that the top USA diplomat in Turkey would visit Brunson later Tuesday.
Hedge funds and other money managers reduced their bullish positions in U.S. crude futures and options in the week ending August 7, data from the U.S. Commodity Futures Trading Commission showed on Friday.
Oil prices rose Tuesday as expectations of weaker Iranian output offset signs of rising global supply.
Some have predicted that Iranian output could drop to as low as 700,000 barrels per day (bpd), from 2 million bpd.
USA energy companies last week increased their number of active oil rigs by the most since May, adding 10 rigs to bring the total count to 869, according to the Baker Hughes energy services firm.
OPEC's output averaged 32.32 million barrels per day in July, up 41,000bpd from June, the group said in its monthly oil market report, citing secondary source figures.
"There are lots of variables in the oil market, the most important of which is Iran", said Tamas Varga, analyst at London brokerage PVM Oil Associates.