The meetings were held on the sidelines of the 16th Summit of Non-Aligned Movement here.
Singh and Karzai reviewed the status of bilateral ties and the importance the two countries attach to the furthering of robust relations in a meeting which lasted for nearly half-an-hour, Foreign Secretary Ranjan Mathai said.
Singh also said he was looking forward to Karzai`s visit to India in November, Mathai said while noting that the two sides are in discussions for the date.
Underlining the need for closer economic relations, the two countries agreed on the "importance of Indian investment in Afghanistan," Mathai said. He said the leaders also agreed on the importance of opposing extremism in any form.
The Prime Minister wished Karzai success in his efforts to complete transition process and assured him that India was a friend of Afghanistan and it will stand by Afghans and its government at this "critical" time of transition.
In his meeting with the Syrian counterpart, Singh was "explained in detail" the ongoing situation in that country and the efforts made by its leadership to undertake reform process.
Al-Halqi also expressed the difficulties faced by the Syrian government because of the continued violence which he said was "instigated" from outside.
Reiterating India`s stand, Singh conveyed that India was in favour of an inclusive political dialogue process which should be Syrian-led and also expressed support to the efforts of UN envoy Lakhdar Brahimi.