BENGALURU, April 28 (Reuters) - Oil prices continued to rise on Tuesday as efforts to end the trade war between the United States and Iran faltered, with the vital Strait of Hormuz remaining almost completely closed, preventing global buyers from accessing energy supplies from key Middle Eastern production areas.

A U.S. official said on Monday that President Donald Trump was dissatisfied with Iran's latest proposal to end the war. Iranian sources revealed on Monday that Tehran's proposal avoided addressing its nuclear program until hostilities ceased and maritime disputes in the Gulf region were resolved.

Trump’s displeasure with the Iranian offer could bring the conflict to a stalemate, as Iran closes the Strait of Hormuz, through which about 20 percent of the world’s oil and gas consumption usually passes, and the United States continues to impose its control over the passage of ships coming from Iranian ports.

Brent crude futures for June delivery rose 45 cents, or 0.4 percent, to $108.68 a barrel by 0051 GMT, after climbing 2.8 percent in the previous session to their highest closing level since April 7. The contract has now risen for seven consecutive days.

U.S. West Texas Intermediate crude for June delivery advanced 58 cents, or 0.6 percent, to $96.96 after rising 2.1 percent in the previous session.

A previous round of negotiations between the United States and Iran collapsed following the failure of direct talks.

“For oil traders, it is no longer rhetoric that matters, but the actual flow of crude through the Strait of Hormuz, and at the moment, that flow remains limited,” said Fawad Razakzadeh, market analyst at City Index and Forex.com, in a note.

He added that even if a solution is reached, production disruptions and logistical challenges mean that recovery could take months.

Ship tracking data revealed significant disruptions in the region, with six Iranian oil tankers forced to turn back due to US control.