They separately also met Brazilian President Jair Messias Bolsonaro and South African President Cyril Ramaphosa for the BRICS meeting. In both these meetings, Modi pitched his idea for a global conference on terrorism, which he had proposed in Maldives earlier this month.
White House spokeswoman Sarah Sanders told reporters Trump and Putin talked about the possibility of a new multilateral nuclear accord between the United States, Russia and China, or an extension of the current US-Russia strategic nuclear treaty.
The Soviet Union took the four southernmost Kuril Islands, which Japan calls the Northern Territories, in the closing days of World War II. The island dispute has prevented the two sides from concluding a postwar peace treaty formally ending the hostilities.
Under pressure from Congress, which last year passed a tough sanctions law targeting Russia, the US Treasury in April imposed sanctions on Russian officials and oligarchs for election meddling and "malign" activities.
The offer Putin described was to permit American law enforcement officials to observe questioning by Russian officials of the indicted Russians in exchange for letting Russian investigators question Americans on other matters.
A European Union report last month said Beijing imposed more new import and investment barriers in 2017 than any other government. The 28-nation EU is China's second-biggest trading partner after the United States.