Mr Singh "highlighted the threat from nuclear proliferation, in particular India's concerns in the context of the proliferation linkages with India's neighbourhood," the foreign ministry said in a statement.
India that has long voiced its concern over the role of Pakistan in helping North Korea develop its nuclear and missile programmes was given an assurance.
"The DPRK (Democratic People's Republic of Korea) side emphasized that as a friendly country DPRK will never allow any action that would create concerns for India's security," the statement added.
Mr Singh's visit, at the invitation of the North Korean government, comes at a time when fresh tension has emerged between the United States and North Korea over America's decision to hold joint military exercises with South Korea.
The North Korean leader has even threatened to pull out of his scheduled meeting with US President Donald Trump next month if Washington continues to unilaterally insist on North Korea giving up its nuclear programme.
India is North Korea's second largest trading partner after China. In April, India had banned all trade with North Korea, except for food and medicines.
The visit comes days after Kim Jong Un travelled to China to meet Xi Jinping, seen along with Trump as the key player in defusing tension in the Korean peninsula.
Last month, Kim Jong Un also held a historic summit with the South last month where the two sides promised peace and de-nuclearisation. Mr Singh reiterated India's support to the joint peace initiative.
Mr Singh's trip comes days before Prime Minister Narendra Modi heads to Sochi for informal talks with Russian President Vladimir Putin. Several international issues on which India has been at variance with the United States like Iran, Palestine and Korea would be discussed at that meeting, according to sources.