Iran’s full re-entry into the global oil market could take months following the lifting of Western sanctions this weekend, one of the country’s top oil officials said on Sunday, signaling that limitations on banking could spell delays.

Iranian officials said the country was preparing to increase production by 500,000 barrels a day. Some of that extra output could be sold immediately through existing contracts with China and other Asian countries. The volume of oil Iran could sell to its former buyers in Europe—where it was...