Iran's return to an already glutted oil market is one of the factors contributing to a global rout in oil prices, which fell below $30 a barrel this week for the first time in 12 years.
Tehran says it could boost exports by 500,000 barrels per day within weeks.
The sanctions deal is viewed with deep suspicion by US allies in the Middle East including Israel and Saudi Arabia. It is, however, supported by Washington's European allies, who joined Obama earlier in his presidency in tightening sanctions as part of a joint strategy to force Tehran to negotiate.
The Obama administration says the deal reached last July offered the best possible prospect of ensuring Iran would not develop a nuclear weapon.
Iran denies its nuclear programme was aimed at obtaining an atomic bomb.