WASHINGTON—Speaker John Boehnerand other senior House Republicans are telling donors and industry groups that they aim to pass immigration legislation this year, despite the reluctance of many Republicans to tackle the divisive issue before the November elections.

Many lawmakers and activists have assumed the issue was off the table in an election year. But Mr. Boehner said at a Las Vegas fundraiser last month he was "hellbent on getting this done this year," according to two people in the room.