In its annual report this week, the center said that Csatáry, who is accused of helping organize the deportation of about 15,700 Jews to the Auschwitz death camp from the Slovakian city of Kassa (Kosice) in 1944, had returned to Hungary from Canada.
Csatáry was the commander of police in Kassa, which was part of Hungary, during World War Two. The center said he had escaped to Canada after the war only to be stripped of his Canadian citizenship in 1997.
Last Friday, Efraim Zuroff, the Israel Director of the Wiesenthal Center, told Reuters a person in Hungary who wished to remain anonymous had tipped it off about Csatáry's whereabouts via email.
"We know where Csatáry is and the information was given to the Hungarian prosecutors... he's in very good health as we know," Zuroff said in a telephone interview.
"We are waiting to see what happens," he added. Gabriella Skoda, a spokeswoman for the Budapest Prosecutors' Office, confirmed in a statement that a war crimes investigation had been launched in September 2011, based on a report from Zuroff. But she did not name a suspect in the statement.
"In the investigation we collect data related to the content of the report," the statement said. "The prosecutors have so far not heard anybody as a suspect in the case."
Since his precise whereabouts in Hungary remain unknown, it was not possible to contact Csatáry for comment. He has not spoken to the media or responded to the allegations against him in the past.
The Wiesenthal Center has spotted several World War Two war crimes suspects in the last decade in its Operation Last Chance.
Another suspect, former Hungarian gendarme officer Sándor Képíró, died at 97 in September in Budapest after a court cleared him of involvement in killing more than 1,000 civilians in the Serb city of Novi Sad in 1942.