Bhaktal, the Indian Mujahideen co-founder, was arrested by Nepali security agencies Wednesday from the heart of Kathmandu and handed over at the Nepal-India border at Raxual, the report said.
Quoting highly placed Nepali intelligence officials, it said Bhaktal was caught at Bagbazar area, taken to Birgunj, a town on Nepal's border with India, and handed over to the Indians.
He was then shifted to Motihari district in Bihar.
According to the report, Bhaktal, one of India's most wanted terrorists, had travelled five times to Kathmandu from Dubai and Pakistan.
Indian security agencies had been keeping a vigil on Tunda, the Laskar-e-Taiba terrorist group's bomb maker, from the time he landed at the Tribhuvan International Airport, the daily said.
He was arrested while coming out of Jama Masjid at Bagbazar in Kathmandu. The man was on a motorcycle.
Tunda reportedly made frequent visits to Jamia IBN Tai Miya Madint Islam Muslim College in Motihari district in Bihar. The institute is located 20 km south of the Nepal-India border.
Nepal Police and home ministry denied the report.
'We do not have any knowledge about these arrests,' Nepal's home ministry spokesperson Shanker Prasad Koirala told IANS.
Although Nepal and India are yet to revisit their bilateral extradition treaty, both sides have agreed to share intelligence to curb terrorism, extremism and criminal elements.
'We have a regular mechanism to share intelligence with our Indian counterparts at any given point of time related to various incidents and personnel,' Nepal Police spokesman Nawa Raj Silwal said.
'But in these particular cases, we do not have any idea that Nepali side handed over them to people on the Indian side,' he said.
Besides these two arrests, Nepal security services recently arrested two Indian sharpshooters and gangsters, Chirinjivi Sagar Kushwaha and Bikash Jha, and handed them over to Bihar Police.
According to police sources, some 400 Indian criminals and those with terrorist links have been arrested so far this year in Nepal. The figure stood at 349 last year.
India and Nepal share a long and porous border, and Indian criminals are known to use Nepal to transit to their countries.