US President Obama and Prime Minister Manmohan Singh have strongly condemned the safe havens for terrorists in Pakistan, calling for their elimination.

In a joint statement issued after their summit, the two leaders have said they are gravely concerned about the threat posed by terrorism and violent extremists emanating from India's neighborhood.

Resolute and credible steps must be taken to eliminate safe havens and sanctuaries that provide shelter to terrorists and their activities.

"The forces of terrorism in our region pose a grave threat to the entire civilised world and have to be defeated. President Obama and I have decided to strengthen our cooperation in the area of counter-terrorism," the PM said.

They have also said it's absolutely imperative to bring to justice the perpetrators of Mumbai attack.

The two leaders also announced a counter-terrorism Cooperation Initiative to expand collaboration on counter-terrorism, information sharing, and capacity building.

"The American people join our Indian friends in remembering the horrific attacks in Mumbai one year ago this week. To prevent future attacks, we agreed that our law enforcement and intelligence agencies will work even closer, including sharing more information." Prime Minister Manmohan Singh said.

Earlier, as he welcomed Prime Minister Manmohan Singh for the first state visit of his administration, US President Barack Obama declared that American ties with India will be "one of the defining relationships" of the 21st century. (Read: India is indispensable to the US, says Obama)

India and the US have signed at least six MoUs on everything from counter-terrorism to education, health, agriculture and clean energy, indicating a consolidation of gains made in the Indo-US relationship over the last few years.

But a crucial fuel reprocessing agreement that will operationalise the landmark Indo-US nuclear deal was left unsigned, in spite of expectations that it would be completed on this visit.