Delta Air Lines will offer a premium economy section on international flights this summer, with more legroom and room to recline — at an additional cost of $80 to $160 each way.

The new seats will be available to book starting in May.

Top-tier frequent fliers and customers who buy full-fare economy tickets will be able to sit in the roomier seats with no extra charge. Lower-level frequent fliers will get discounts on the seats.

The seats, in the first few rows of coach, are similar to those offered by Delta Air Lines Inc. partner Air France-KLM. Those provide as much as 6 inches of additional legroom. Those who pay extra for Delta’s new seats will also get to board early and get free alcoholic drinks in-flight.

Several other airlines offer premium economy seats for a fee, including United Airlines and Virgin Atlantic.

Premium economy seats are a move by airlines to attract business travelers, some of whom have opted for coach to save money.

Delta says some business-class travelers are coming back, and it’s adding more special seats for them, too. The airline also said Monday that it plans to install 34 flat-bed Business Elite seats along the aisles of 32 A330 aircraft within the next two years. The latest move means that Delta will have Business class seats that convert to beds on all of its big international planes, more than 150 of them, by 2013.