The party targeted Home Minister P Chidambaram alleging he is responsible and the Home Ministry is a "total failure".
The name of Feroz Abdul Khan, alias Hamza, an accused in 1993 Mumbai blast case who was arrested from a village in Navi Mumbai in February last year and handed over to CBI, is contained in the list of most wanted by India and he was found in Arthur Road jail in Mumbai.
BJP president Nitin Gadkari said "It is a failure of the Home Ministry and the way in which it has been happening. It is very unfortunate and shameful for the country."
He said the goof-up is an "embarrassment" for the country.
"The international community will not take our case seriously," he added.
When it was pointed out that CBI is under DoPT, Gadkari said "This indicates how our agencies are working and how our government is working."
Taking on CBI, he charged "The agency is only blackmailing political parties.They have acted against the opposition leaders. This is only protecting the interests of Congress party."
CBI is "Congress Bureau of Investigation", he said and alleged the agency is protecting the intersts of the ruling party.
The BJP chief alleged the "Home Ministry is a total failure and the Home Minister is responsible (for the goof-up)."
Seeking an explanation from Home Minister, Gadkari said "It is time for Chidambaram to explain all this as it is a security matter and a serious matter. The matter relates to national interest and the way government is dealing with such a case, it indicates that investigating agencies are so politicised."
Earlier, Wazhur Kamar Khan, whose name had also figured in India's most wanted list, was traced in Mumbai, in the first case of the goof-up.