WASHINGTON—Iraq’s latest push to retake the Sunni city of Tikrit from Islamic State extremists has thrown a new spotlight on the role being assumed by Iran in assisting Baghdad in its fight to regain control of the country.

U.S. officials said Iran is supporting the offensive to retake Tikrit, supplying artillery, rocket fire and aerial drones. Islamic Revolutionary Guard Corps, or IRGC, fighters were on the ground with Iraqi units, mostly operating artillery and rocket batteries, according to a U.S. military official.

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