But he followed up the compliment with a small gaffe. Putin assigned the wrong number to the presidency of Bush's father, former President George H.W. Bush.
"We had a very nice fishing party this morning," Putin said. "We caught one fish, but that was a team effort, and we let it go to the captain."
He was referring to Bush's 83-year-old dad, who was at the wheel of the boat. Putin mistakenly said he was the 42nd president of the United States, not the 41st.
Neither Bush seem bothered, and the current president said it was "very thoughtful" of Putin to share credit for the catch.
"A fine catch," the president said about the striped bass that his father said was about 30 inches (76.2 centimeters) long.
You had to take the former president's word for it.
"Mind you, the fish that we caught, we've let it free," Putin said.