Bolton extended the invitation to Putin on Thursday, a National Security Council spokesperson told CNN.
Russia’s ambassador to the U.S. said Moscow is ready to discuss a possible visit to Washington.
Ambassador Anatoly Antonov said Friday that Russia “was always open to such proposals. We are ready for discussions on this subject.”
However, Antonov said it is up to the Kremlin to formally respond.
The Kremlin has not commented on Trump's proposal.
The news of another meeting between the two leaders seemed to surprise Dan Coats, the U.S. Director of National Intelligence.
During a live Q&A at the Aspen Security Forum in Aspen, Colorado, MSNBC host Andrea Mitchell interrupted their chat to announce the breaking news when it happened.
“The White House has announced on Twitter that Vladimir Putin is coming to the White House in the fall,” Mitchell said.
“Say that again?” Coats asked as the crowd bursts into laughter.
After a few moments, Coats said, “OK. That’s going to be special.”
Coats also said during the forum that he does not know what the two world leaders discussed during the summit in Helsinki.
The Associated Press contributed to this report