Centanni and New Zealander Wiig who work for the US broadcaster Fox News were seized by masked gunmen in Gaza City in August 14.
Ken Centanni told Aljazeera that the American was in Gaza to reflect the truth and had always respected the Palestinian people and their culture.
"I want his captors to know that Steve is an honourable man and always attempts to do what is right", he said.
"Steve will be more useful for the Palestinians if he is a free journalist rather than a hostage," he added.
No one has claimed responsibility for the kidnapping of the two journalists.
"We love Steve so much. His health, safety and life are your responsibility now," Centanni's brother said. "Please, contact our family, tell us that he is alive and has not been harmed."
Wiig's wife made a similar appeal in Gaza on Wednesday.
Mahmoud Abbas, the Palestinian president, and Ismail Haniya, the prime minister, have ordered all security agencies to search for the two men and secure their release.
An ambassador from New Zealand also said on Sunday that he was "very concerned" about the journalists, and urged their kidnappers to release them.
Olaf Wiig's wife held a protest in
Gaza City over his kidnapping
Peter Ridder spoke outside Haniya's office in Gaza City shortly after the two men met. "Just like the family, we are very concerned about the safety and security of the hostages, and we are working together to try to secure their safe return," he said.