“Nightline” has gotten a lifeline. After a bitter week last month in which his network offered his time slot to CBS “Late Show” host David Letterman (who declined the invitation), ABC and Ted Koppel seem to have struck an agreement that will keep the late-night news program, “Nightline,” on the air through 2003, reports Tuesday’s New York Times. The agreement may not cover all of Koppel’s contract, which has almost four years left on it, according to The Times, but Koppel and his top producers, Tom Bettag and Leroy Sievers, are “satisfied” with the turn of events: “We’re very content,” they said in a statement. In a statement Monday, Robert A. Iger, president of ABC parent Disney, said: “We want to renew and reaffirm our support for ‘Nightline,’ ” adding, “We look forward to working with ABC News to make a strong program even stronger in the coming years.” In his statement, Koppel said, “For our part, my colleagues and I renew our commitment to making ‘Nightline’ the best news program it can possibly be. It is especially gratifying for me and everyone at ‘Nightline’ to have questions about the future of the broadcast so warmly and enthusiastically resolved at the highest levels of the corporation.” News of ABC’s desire to have Letterman supplant Koppel had sparked questions about Disney’s commitment to serious news programming. Disney executives at the time said they were simply fulfilling their obligation to seek the most profitable programming for their network. Meanwhile, say news reports this week, Letterman, who turns 55 this Friday, and Koppel, 61, have no animosity between them — and each has promised to appear on the other’s show. Letterman is remaining with CBS.