By Scott DiSavino

NEW YORK (Reuters) - Oil prices gained about 1% on Tuesday, with U.S. crude settling at a 13-week high on supply concerns, including no nuclear deal with Iran, and prospects for demand growth in China, which is relaxing lockdowns to control the pandemic.

Looking ahead, analysts polled by Reuters forecast U.S. crude inventories fell last week. A drop in crude stockpiles could further support prices. [EIA/S] [API/S]

The American Petroleum Institute (API), an industry group, will issue its inventory report at 4:30 p.m. EDT (2030 GMT) on Tuesday. The U.S. Energy Information Administration (EIA) reports at 10:30 a.m. EDT (1430 GMT) on Wednesday.

Robert Yawger, executive director of energy futures at Mizuho, said "several numbers" in the EIA report are "within striking distance of historical lows," including possibly crude storage for the country, crude storage at Cushing, Oklahoma and crude storage in Strategic Petroleum Reserve.

Brent futures gained $1.06, or 0.9%, to settle at $120.57 a barrel, its highest since May 31. U.S. West Texas Intermediate (WTI) crude gained 91 cents, or 0.8%, to $119.41, its highest settlement since March 8 which matched an August 2008 settlement high.

The United States said Iran's demands on sanctions-lifting were preventing progress on revival of the 2015 nuclear deal. Analysts have said a deal could add 1 million barrels per day of world oil supply.

The U.S. EIA projected U.S. crude production and petroleum demand will both rise in 2022. [EIA/M]

Prices also drew support from expectations demand would recover in China, where the capital Beijing and commercial hub Shanghai have been returning to normal after two months of lockdowns.

Also, analysts doubted global oil supplies would rise much following last week's OPEC+ decision to bring forward production increases.

The quota increase from OPEC+, the Organization of the Petroleum Exporting Countries (OPEC) and allied producers including Russia, is lower than the loss of Russian crude resulting from Western sanctions, analysts said, adding that it also fails to address a shortage in oil products.

Trafigura's CEO said oil prices could soon hit $150 a barrel and go higher this year, with demand destruction likely by the end of the year.

Goldman Sachs increased its Brent oil price forecasts by $10 to $135 a barrel for the period between the second half of 2022 and the first half of next year, citing an unresolved structural supply deficit.

In other supply concerns, the Sharara oilfield in Libya was halted again late on Monday and in Norway, more than one in 10 offshore oil and gas workers plan strike action from Sunday if state-brokered wage mediation fails.

(Additional reporting by Rowena Edwards in London and Isabel Kua in Singapore; Editing by Louise Heavens, David Goodman, David Gregorio and Mark Porter)