The prime minister’s comments came at the end of a brief visit to Mumbai, where 179 people were killed and hundreds injured in several bomb blasts this week.
Singh said: “We have to recognise that the terrorists are trying to spread their tentacles across the country.
“We are also certain that these terrorist modules are instigated, inspired and supported by elements across the border without which they cannot act with such devastating effect.
“Pakistan in 2004 had solemnly given an assurance that Pakistani territory will not be used to promote, encourage, train and abet terrorist elements directed against India.
“That assurance has to be fulfilled before the peace process or other processes can make progress.”
Pakistan has rejected Singh’s claims.
Tasnim Aslam, a Pakistan foreign office spokeswoman, said: “These allegations are unsubstantiated, we have already rejected them.”
Earlier on Friday, A N Roy, Mumbai’s police commissioner, named a man known only as Rahila as a third suspect in the attacks.
On Thursday, India’s anti-terror squad released photographs of two other suspects, Sayyad Zabiuddin and Zulfeqar Fayyaz.
The nationalities of the men were not given.
Pakistan-based Islamic militant group Lashkar-e-Tayyaba, which operates in Kashmir, is the prime suspect.