Appearing before cameras on the second day of a two-day visit to New Delhi on Wednesday, Aziz gave journalists no hints as to what might be achieved.
Differences over Himalayan Kashmir have bedevilled the two countries for more than 57 years and even led to two out of their three wars.
South Asian affairs commentator Pran Chopra said the meeting was "an attempt to try and put the peace process back on track".
Aziz's visit comes after diplomatic sparks flew last week when Singh ruled out any redrawing of India's borders or a further division of Kashmir, spiking a set of proposals by Pakistani President Pervez Musharraf.
Musharraf suggested last month that Kashmir should be demilitarised and that India and Pakistan should agree on a compromise over its disputed status.
The outcome could be joint control, some form of UN control or independence.
This received a cool response from New Delhi although India has started to withdraw some troops from Kashmir, citing a decline in guerrilla violence in the region.
India accuses Pakistan of abetting the 15-year-old revolt in its only Muslim-majority state of Jammu and Kashmir that has killed more than 40,000 since 1989.
Islamabad denies the charge, but says it provides moral support to the "legitimate aspirations" of Kashmiris.
The second issue for discussion - a gas pipeline running from Iran to India - has also shown no discernible progress.
Aziz met Indian Oil Minister Mani Shankar Aiyar to discuss the longstanding plan to build a gas pipeline to run through Pakistan.
But Aiyar linked the pipeline issue to wider trade issues. "It shouldn't be that in one field we race ahead and not in others," he said.
New Delhi has urged Pakistan to expand trade links, including granting most favoured nation status to India.
But Islamabad says resolving the dispute in Kashmir would help to boost economic ties.
It has been pushing for the gas pipeline, which could earn it millions of dollars in annual revenues.