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.
Singh said on Monday that he had asked Abdullah to use his "good offices" with Pakistan to urge it to check what he called cross-border terrorism targeting India.
He stressed that India had not asked for mediation.
"I know Saudi Arabia has close relations with Pakistan. I did discuss the Indo-Pak relations with his majesty on a one-to-one basis," Singh said.
"I explained to him the role that terrorism - aided, abetted and inspired by Pakistan - is playing in our country. And I did not ask for him to do anything other than to use his good offices to persuade Pakistan to desist from this path."
Singh seemed to be under pressure to clarify the subtle difference between "good offices" and "mediation" after the opposition Bharatiya Janata Party attacked an accompanying junior foreign minister's remarks that were construed as seeking Saudi mediation with Pakistan.
That interpretation was denied by the minister, Shashi Tharoor.
Rahul Roy Choudhury, an expert in South Asian affairs, told Al Jazeera: "For the first time India and Saudi Arabia really sat together to discuss concerns emanating from Pakistan."
"I think the common theme in these discussions, is how best do India and Saudi Arabia work together to counter extremism and terrorism ... it is an area where India and Saudi Arabia seem to have common concerns," he 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 holds Lashkar-e-Taiba, an armed Pakistani group, responsible for the assault.
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.