New York (CNN) -- Four New York Times journalists missing in Libya have been captured by pro-government forces but will be released, the newspaper reported Friday.

The Times cited an interview given by Libyan leader Moammar Gadhafi's son, Saif al-Islam Gadhafi, to ABC's Christiane Amanpour late Thursday, a transcript of which was posted on ABC's website.

In it, the younger Gadhafi says photographer Lynsey Addario will be released.

He tells Amanpour that security forces arrested her because she had entered the country illegally, "but then they were happy because they found out she is American, not European. And thanks to that, she will be free tomorrow."

While Gadhafi did not mention the other three missing journalists, the Times said Libyan government officials told the U.S. State Department on Thursday evening that all four would be released.

The paper also said the Libyan government allowed the journalists to call their families Thursday evening.

"We're all, families and friends, overjoyed to know they are safe," the paper quoted its executive editor, Bill Keller, as saying. "We are eager to have them free and back home."

CNN could not independently confirm promises to release the journalists.

Saif al-Islam Gadhafi does not speak for all parts of the Libyan government.

The newspaper identified the journalists as Anthony Shadid, its bureau chief in Beirut, Lebanon, and a two-time Pulitzer winner for foreign reporting; Stephen Farrell, a reporter and videographer who was kidnapped by the Taliban and rescued by British commandos in 2009; and Tyler Hicks and Addario, photographers who have covered the Middle East and Africa.

Addario is an experienced war photographer based in India who recently won a MacArthur Fellowship -- known as a "genius grant" -- for her photography around the world.

Hicks, a staffer for the paper, is based in Istanbul and has served as an embedded journalist in Afghanistan.

The four journalists entered the rebel-controlled eastern region of Libya via the Egyptian border without visas to cover the civil war in the country, the Times said.

Editors at the paper said they had last been in touch with the journalists Tuesday morning. The paper said that after it reported losing contact, the Gadhafi government pledged that if the four had been detained by the government's military forces, they would be located and released unharmed.