A Meeting by the River received professional ratings from Allmusic, Chicago Tribune, and Rolling Stone.
Allmusic  Chicago Tribune  Rolling Stone  Peter Margasak of the Chicago Tribune awarded the album four stars out of four, describing Cooder's performance as "arresting" and Bhatt's as "haunting". Rolling Stone called the album "fruitful" and awarded it three stars out of five. Allmusic's Daniel Gioffre described the instrument as a hybrid between a guitar and a vichitra veena; it is played with a metal slide moving across steel rods along the neck. Gioffre wrote a positive review of the album and called Cooder and Bhatt "genuine masters" of their respective instruments. 
