Addressing a BJP rally here, he also accused the Congress government in Karnataka of trying to 'divide' the society and lashed out at it on the law-and-order front, citing the killings of right-wing activists and journalist Gauri Lankesh.
The senior BJP leader posed several questions to Rahul Gandhi, who made the charge after being handed over the baton by his mother Sonia Gandhi yesterday to take over as the Congress president, heralding a generational change.
Mr Singh said, "Congress has got a new president. I congratulate him. He says that BJP is responsible for the unrest in the country. I want to ask him who is behind the communal tensions, terrorism, Naxalism and unrest in Kashmir?
"Who is behind the dynastic politics in the country? Let Rahul Gandhi know that it is BJP which is trying to douse the fire lit by Congress," Mr Singh said.
He also said the "whole world knew that the BJP alone knows how to run the nation. The Gujarat and Himachal Pradesh election results (tomorrow) will prove it again. Already exit polls have predicted that we are going to form the government in these two states," he said.
In his first speech to party workers after formally assuming charge as Congress president, Rahul Gandhi had said:"They break, we unite. They ignite fire, we douse it. They get angry, we love. This is the difference between them and us."
Targeting the Siddaramaiah-led government in Karnataka, Mr Singh said the Congress regime believed in "spreading enmity" between different communities.
Referring to the killing of RSS activist Rudresh here early this year and VHP leader D S Kuttappa in Kodagu district in NOvember, 2015 and 19-year-old Paresh Mesta recently, he said they were "murdered in cold blood." Even Gauri Lankesh was killed.
"If we come to power in Karnataka, we will get these cases thoroughly investigated," the Union Home Minister said.
Ms Lankesh was shot dead by unidentified assailants here in September, leading to a national outrage.
Mr Mesta, who was from the fishermen community, was found dead under mysterious circumstances in Uttara Kannada district, leading to violence last week.
The state government has ordered a CBI probe into Mr Mesta's death, for which the BJP has blamed the "jihadi elements".
Accusing the Congress of dividing the society, Mr Singh said when there was a controversy surrounding the 18th-century ruler of Mysuru, Tipu Sultan, the state government should have refrained from celebrating his birth anniversary.
"There were many other historical characters for celebrating their birthdays such as Kittur Rani Chennamma, the founder of Bengaluru, Kempe Gowda, and (renowned engineer) Sir M Visvesvaraya. The Karnataka government wants to divide the Indian society," he added.
Singh said the Karnataka government gave reservations to Muslims, even though there was no such provision in the Constitution.
"Reservation based on religion is a deception with the people of the state. The Constitution does not allow it," he added.
The Union minister said the country was scaling new heights under the leadership of Prime Minister Narendra Modi.
"Despite the GST (Goods and Services Tax) and demonetisation, various international economic organisations have projected a high economic growth rate for the country. They have even recommended such economic reforms," he added.
Regarding border security and internal peace, Mr Singh said the way the Dokalam stand-off with China was resolved showed that India was a strong country.
"Even China realises that India is not the same anymore," he added.
Mr Singh said the country had taken the terrorists in Kashmir head-on and curbed their activities substantially.
Karnataka's growth would be rapid if the BJP was voted to power in the state, he added.
Speaking on the occasion, state BJP chief B S Yeddyurappa too slammed Chief Minister Siddaramaiah for allegedly talking about Prime Minister Narendra Modi in a derogatory manner.
"You (Siddaramaiah) are only a 'bachcha' (kid) in front of Prime Minister Modi. When the whole world is admiring Modi, who are you to talk about him in an insulting way," the former Chief Minister said.
The BJP rally here was organised as part of "Parivarthan Yatra" with the party leaders crisscrossing the state to "expose the misdeeds" of the Siddaramaiah government ahead of the Assembly polls, due early next year.