"If not today then tomorrow, one side will have to take the first step. We have always spoken of friendship but they should take some friendly action," Rajnath Singh said at the 12th Hindustan Times Leadership Summit.
Both Prime Minister Narendra Modi and his Pakistani counterpart Nawaz Sharif would be attending the South Asian Association for Regional Cooperation (Saarc) summit in Kathmandu.
Rajnath Singh blamed Pakistan for terrorism, saying terror in India was not home-grown but sponsored by the neighbouring country.
He rejected Islamabad's contention that non-state actors were behind the terrorism.
"I want to ask Pakistan: 'Is ISI (Inter-Services Intelligence) also a non-state actor'," he said.
He linked the ISI with supporting terrorists - ranging from Osama bin Laden to Hafiz Saeed and underworld don Dawood Ibrahim and the accused in the 26/11 Mumbai attack.
"Who helped Osama bin Laden? Who is helping Hafiz Saeed? We have requested Pakistan to act against them (Mumbai attack mastermind) but they drag their feet," he said. "So we say that terrorism is completely Pakistan-sponsored."
He also said terrorism in India was being externally aided by Pakistan.
On the firing along the border, Rajnath Singh said India's "tough stance" had paid dividends.
When Pakistan did not stop ceasefire violations despite the Border Security Force showing the white flag 16 times, the home minister told the forces to hit back hard.
"As you saw, Pakistan had to go to the UN to say that you intervene, you intervene. In other words, it raised a hue and cry," he said.
Rajnath Singh also said the Achik National Volunteer Council (ANVC), an insurgent group in Meghalaya, has agreed to give up arms.
"There are numerous insurgent groups in the northeast whom the government has encouraged to lay down their weapons, and there is an integrated action plan to deal with the threat of Maoism," he added.
Rajnath Singh said cyber crime was a big challenge for India, and one of the hurdles being faced was due to servers not being in India. He said they have a mechanism in place to deal with that.
He said India was building roads and developing infrastructure along the border despite stiff objections from China and Pakistan.
With many parts of the country's borders still porous, India was trying to make greater use of technology to ensure security along its borders, he said.
He was of the view that his government has many challenges, and since India has a federal structure, they would need the support of the states.