The tournament, starting Friday, assumes significance as the shooters will be competing at the same venue which will host the events during Olympics and will get a feel of it.
"My gratitude to @SushmaSwaraj and @AmbGurjitSingh for intervening and working towards getting things done," Bindra, India's lone Olympic gold medallist, wrote on his twitter handle.
Almost all the shooters (pistol/rifle/shotgun) representing India in 2016 Rio Olympics are taking part in the event in the Brazilian city.
Bindra had earlier tweeted, "@SushmaSwaraj and are stuck. Need your help in order to secure a new travel document and Brazil visa to be able to compete successfully."
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Swaraj then asked the Indian Embassy in Germany to look into the matter. And India's Ambassador to Germany Gurjit Singh ensured the matter was resolved swiftly.
The 33-year-old Bindra, who clinched a historic gold in men's 10-m air rifle at Beijing Olympics in 2008, thanked Swaraj for her gesture.
The union minister, on a lighter note, reminded the shooter that "our demand for Olympic Gold Medal stands".