Singh told Saudi Arabia's quasi-parliament, the Shura Council. that New Delhi will go the "extra mile" to improve relations with neighbour Pakistan.
"If Pakistan co-operates with India, there is no problem that we cannot solve and we can walk the extra mile to open a new chapter in relations between our two countries," Singh said.
New Delhi broke off talks with Islamabad following the 2008 attacks on Mumbai, in which armed men launched assaults in India's financial capital, killing 166 people.
India accuses Lashkar-e-Taiba, an armed Pakistani group, of being responsible.
The two countries held talks last Thursday for the first time in more than a year, but they have yet to resume a formal peace process.