Later during the day, Singh is due to address the Council on Foreign Relations and the Woodrow Wilson International Centre.
Singh told The Washington Post and Newsweek ahead of his arrival that it was important for US forces to remain in Afghanistan and called on Obama to pressurise Pakistan to rein in Islamic extremism.
"We have been the victims of Pakistan-aided, abetted and inspired terrorism for nearly 25 years. We would like the United States to use all its influence with Pakistan to desist from that path," Singh said in the interview.
"Pakistan has nothing to fear from India. It's a tragedy that Pakistan has come to the point of using terror as an instrument of state policy"
India's prime minister
"Pakistan has nothing to fear from India. It's a tragedy that Pakistan has come to the point of using terror as an instrument of state policy," he said.
While Pakistan has acknowledged that armed groups have operated from its soil, Islamabad denies they are acting on behalf of the state.
Singh said he hoped Obama would complete an accord championed by George Bush, the former US president, to end India's decades of pariah status on civilian nuclear energy markets.
Both houses of the US Congress approved resolutions welcoming Singh and calling for greater co-operation with India.
The unanimity symbolised a change from just a few years ago, when some legislators fought the nuclear deal because of India's refusal to sign the Non-Proliferation Treaty.
India and the US have also urged each other to commit to more action ahead of next month's high-stakes Copenhagen climate change summit.