Boeing did not disclose the name of the buyer or the buyers of the short- to medium-haul aircraft in the week through March 18.
The Chicago-based company said it had a total of 176 net new orders since the year started, including 170 orders for the single-aisle 737.
A Boeing spokesman said that 40 of the 71 new 737 orders were for the 737 MAX, a new, re-engined model that will improve fuel efficiency. He said the future airplane already has more than 1,800 orders.
The 737 MAX is Boeing's response to European rival Airbus's new A320Neo.
The first flights of both planes are scheduled in 2016, with deliveries to customers beginning in 2017.
Boeing said it had completed Wednesday its first Next-Generation 737 made at the increased production rate of 42 airplanes per month. Due to continued strong market demand for jetliner, it plans to ramp up production to 47 airplanes a month in 2017.
Copyright Agence France-Presse, 2014