BENGALURU, April 28 (Reuters) - Oil prices extended their gains on Tuesday as efforts to end the U.S.-Iran war appear stalled, with the crucial Strait of Hormuz waterway still mainly shut, keeping energy supplies from the key Middle East producing region out of the reach of global buyers. 

U.S. President Donald Trump is unhappy with the latest Iranian proposal aimed at ending the war, a U.S. official said on Monday. Iranian sources disclosed on Monday that Tehran's proposal avoided addressing its nuclear program until hostilities cease and Gulf shipping disputes are resolved.

Trump's displeasure with the Iranian offer leaves the conflict deadlocked, with Iran shutting shipping flows through the Strait of Hormuz, which typically carries supply equal to about 20% of global oil and gas consumption, and the U.S. keeping in place its blockade of Iranian ports. 

Brent crude futures for June climbed 45 cents, or 0.4%, to $108.68 a barrel as of 0051 GMT, after gaining 2.8% in the previous session to its highest close since April 7. The contract is up for a seventh day. 

U.S. West Texas Intermediate (WTI) crude for June rose 58 cents, or 0.6%, to $96.96, after gaining 2.1% in the previous session.

An earlier round of negotiations between the U.S. and Iran collapsed last week following failed face-to-face talks. 

"For oil traders, it's not the rhetoric that matters any more, but the actual physical flow of crude oil through the Strait of Hormuz, and right now, that flow remains constrained," Fawad Razaqzada, market analyst at City Index and FOREX.com, said in a note.

Razaqzada added that even if a resolution is reached, production outages and logistical challenges mean recovery could take months.

Ship-tracking data revealed significant disruptions in the region, with six Iranian oil tankers forced to turn back due to the U.S. blockade.

However, a liquefied natural gas tanker managed by the United Arab Emirates' Abu Dhabi National Oil Co did cross the Strait of Hormuz and appears to be near India, ship-tracking data showed on Monday.

Prior to the U.S.-Israeli war on Iran, which began on February 28, between 125 and 140 vessels transited the strait daily.