The two Sufi clerics, who went missing in Pakistan last week, on Monday thanked the governments of India and Pakistan for their safe return here but remained tightlipped on what led to their disappearance.
Nazim Ali Nizami, one of the clerics, did reject Pakistani media reports that they were in "interior Sindh where there was no communication network".
"We did not have visa for Sindh interior region, so how could we have gone there? We come from the school of sufi which teaches peace and brotherhood. There are good and bad elements and those who go against the teachings they have to suffer humiliation," he told reporters, without elaborating further.
When asked as to why they were "interrogated", Nazim said they were asked about their visa and other immigration details.
Both Nazim and Syed Asif Nizami, who is the the head priest of Hazrat Nizamuddin Dargah, "thanked" the Indian and the Pakistani governments for their return to the homeland.
"We thank Union Home Minister Rajnath Singh and External Affairs Minister Sushma Swaraj and well-wishers from all religions who prayed for our return," they told reporters.
The two are likely to meet Swaraj on Monday.
Amir Nizami, son of Syed Asif Nizami, alleged that the duo were "taken away" based on a news report in a local Urdu daily which claimed that they had links with Indian intelligence agency RAW.
Asked if Pakistan spy agency ISI was involved in the episode, he refused to comment but made it clear that "no force was used" against them.