Oil prices moved sharply higher on Tuesday, amid dwindling hopes of a U.S.-Iran deal to fully reopen the Strait of Hormuz, despite Washington's fresh efforts to boost fuel flows.

U.S. West Texas Intermediate futures were 2.7% higher at $84.36 a barrel at 4:30 a.m. ET, at their highest level this month. International benchmark Brent crude was up 2.53% at $89.94 a barrel.

The Trump administration on Monday extended its suspension of a shipping law restricting the transport of goods between American ports to U.S. vessels, while narrowing the waiver only to vessels hauling certain energy resources.

The move came after data showing U.S. crude oil stockpiles have fallen to their lowest level in more than four decades

Oil prices moved sharply higher on Tuesday

Traders are meanwhile assessing the latest contradictory statements coming from Washington and Tehran, with President Donald Trump stating the U.S. has "100%" control of the Strait of Hormuz.

A fresh sticking point has emerged over the payment of reparations, which are now being demanded by both sides over claimed damages.

"The oil market remains very headline-driven, which leaves prices whipsawing. The latest bout of optimism is quickly fading," ING strategists wrote in a Tuesday note.

"Current rhetoric suggests any potential deal is still some way off, meaning risks remain skewed to the upside for oil prices."

— CNBC's Kevin Breuninger and Spencer Kimball contributed to this report.