El Mundo newspaper correspondent Javier Espinosa, 49, and freelance photographer Ricardo García Vilanova, 42, were seized on September 16th, the latest of scores of journalists captured while covering Syria's civil war.
"We believe they are alive and we believe they are well," El Mundo's director Pedro J. Ramírez told a news conference in Madrid.
A spokesman for the two men's families, Gervasio Sánchez, added: "We are convinced that they are alive. They were alive and well a month ago," the last time their relatives had news of them from witnesses.
El Mundo identified the captors as members of the Islamic State of Iraq and the Levant, a jihadist faction in Syria with roots in Al-Qaeda's Iraqi affiliate.
El Mundo said it had kept the kidnapping quiet until now while it contacted the captors via intermediaries. The kidnappers have still not made any demands.
"Unfortunately, these gestures have yielded no result and we have concluded, the families in agreement with the newspaper, that the time has come to share our concern and indignation" publicly, Ramirez said.
The two journalists last made contact with the newspaper "a few hours" before they were kidnapped, he added.
"Since then their families and the newspaper have learned that there have been some people who have seen them and who believe that they are well," he said.
The people who saw the two journalists were able to confirm that the kidnappers belonged to the Islamic State of Iraq and the Levant, he added without giving further details.
"The kidnappers have not made public, or conveyed to the families or the newspaper, any specific demand. Given this unwillingness for dialogue or contact, we decided to break the information blackout."
Ramirez called for the kidnappers "to immediately free" Espinosa, Garcia and a third Spanish journalist, Marc Marginedas, a correspondent for Catalan daily El Periódico who went missing on September 4th.
Espinosa's wife Monica Prieto, who is also a prize-winning journalist, echoed the call in a separate news conference earlier in Beirut.
"We believe the Syrian people need our work, and that we must live up to our responsibility," she said.
"But you, as Syrians, also have a responsibility towards all those, Arabs and Westerners, who have defended you."
Espinosa has been a Middle East correspondent for El Mundo since 2002, based in Beirut.
Like García, he has covered some of the most dangerous points in the Syrian conflict, including the siege of Homs in February 2012.
On February 22nd he escaped that bloodbath in which human rights groups said 700 people were killed and thousands injured, and made it back to Lebanon a week later.
Among those killed in Homs were two other Western journalists: US reporter Marie Colvin and French photographer Remi Ochlik.
Espinosa wrote of his escape from the city, under fire among a crowd of wounded refugees, in a compelling reportage published on March 3.
García Vilanova has worked for media such as the New York Times, the Washington Post and Agence France-Presse, for whom he has contributed reports from Libya and Syria.
Media rights campaign group Reporters Without Borders ranks Syria as the most dangerous country in the world for journalists.
Twenty-five journalists have been killed there since the start of the conflict in early 2011, and a similar number are missing or detained, it estimated last month.
On Tuesday, Reporters Without Borders condemned the abduction of García Vilanova and Espinosa.
The abduction "again highlighted the ISIS strategy of trying to end the presence of all foreign journalists in the regions it controls or aspires to control," said the group in a statement.