"We have absolutely no information" on Fr. Tom Uzhunnalil, said Fr. Mathew Valarkot, spokesman for the Salesians' Bangalore province, to which the kidnapped priest belongs. His remarks were reported by ucanews.com.
Suspected Islamic terrorists took away the priest after they attacked a home for the elderly operated by the Missionaries of Charity in Aden and gunned down some 16 people, including four nuns.
Vatican diplomats also are working to locate the priest and secure his release, ucanews.com reported. Valarkot said the Salesians have been pressuring the government for answers.
"But even today, we do not know who has taken him and what their motives are because no one has claimed responsibility," Valarkot said.
Messages on social media have claimed that Islamic State agents kidnapped the priest and are torturing him. An undated and unnamed message also said the kidnappers plan to crucify the priest on Good Friday.
"These are all rumours. When no one has claimed responsibility for the kidnapping, how do we know other details?" Valarkot said.
The Church is in "constant touch" with the government on Uzhunnalil, said Fr. Joseph Chinnayan, deputy secretary-general of the Indian Catholic bishops' conference. The foreign ministry has "informed us that they have stepped up efforts to locate the priest."
Valarkot urged patience, noting that an Indian Jesuit kidnapped by Islamic terrorists in Afghanistan was released after nine months following Indian government efforts. Jesuit Father Alexis Prem Kumar was kidnapped in June 2014. Media reports credited hectic but quiet diplomatic efforts with securing his release the following February.