The invitation was extended by visiting Indian National Security Adviser Ajit Doval who met with the president in Kabul on Monday.
During the meeting, the sides discussed regional cooperation and fight against terrorism.
They hoped that the new U.S. strategy would lead to peace and stability in the region.
The sides also emphasized on continuation of strategic cooperation between the two countries in different areas.
During the visit, Doval also met with Chief Executive Abdullah Abdullah and his Afghan counterpart Mohammad Hanif Atmar.