The invitation was extended during a telephonic call Singh made to Obama last evening to congratulate him on his re-election.
During his first term, Obama undertook a visit here in November 2010 when he announced support for India's bid for a permanent seat in the UN Security Council.
The two countries had also agreed on a number of new initiatives, including cooperation in internal security, removal of Indian companies from the US sanctions' list and setting up of a research centre in India in civil nuclear field.
The two countries signed deals worth $10 billion.
Singh and Obama, who met several times over the last four years at various places in the world, would have an opportunity to have a meeting in Phnom Penh on the sidelines of ASEAN Summit on November 19.
In the course of the telephonic interaction last evening, "both leaders expressed their intention of seeing each other soon", a PMO statement said.
The Prime Minister told Obama that his re-election had given the opportunity to the two countries to carry forward and build on the "enormous successes" achieved in bilateral ties in the last few years.
While thanking Singh, Obama described him as "a wonderful partner" whose leadership at the world stage he appreciated and said he looked forward to working together.