10 Apr 2021 / 09:00 H. * Deal sees OPEC+ output rising 350,000 bpd from May * Gradual rise in OPEC+ production continues in June, July * U.S. energy secretary, Saudi energy minister hold call (Adds details, end of meeting) By Alex Lawler, Rania El Gamal and Vladimir Soldatkin LONDON/DUBAI/MOSCOW, April 1 (Reuters) - OPEC+ agreed on Thursday to gradually ease its oil output cuts from May, sources said, after the new U.S. administration called on Saudi Arabia to keep energy affordable, mirroring Donald Trump's practice of calling OPEC's leader over oil policy. The group, which has been implementing deep cuts since oil prices collapsed in 2020 due to the coronavirus crisis, agreed to ease production cuts by 350,000 barrels per day (bpd) in May, another 350,000 bpd in June and further 400,000 bpd or so in July.