US President Donald Trump held a summit with Putin in Helsinki, the Finnish capital, and then issued Putin an invitation to visit Washington in the autumn. But that was postponed after Trump faced allegations of cozying up to the Kremlin.
Mr Bolton, speaking at a news conference during a visit to ex-Soviet Georgia, days after meeting Putin and senior security officials in Moscow, said: ”We have invited President Putin to Washington.”
US broadcaster RFE/RL said during his trip to Moscow Mr Bolton said he gave Putin an invitation to visit next year.
It was not immediately clear if Putin had accepted the invitation. Putin last held a meeting with a US President on American soil in 2015 when he met Barack Obama on the sidelines of a UN General Assembly.
Mr Trump’s earlier invitation to Putin sparked an outcry in Washington, including from lawmakers in Mr Trump’s Republican party, who argued that Putin was an adversary not worthy of a White House visit.
The topic of Putin visiting the US is a highly-charged one, because US intelligence agencies allege that Russia interfered in the 2016 presidential election to help Mr Trump win. Russia denies any election meddling.
The US President has said it is in US interests to establish a solid working relationship with Putin.
The two leaders plan to hold a bilateral meeting in Paris on November 11 on the sidelines of events to commemorate the centenary of the end of World War One.
Mr Bolton said the Paris meeting would be brief.
The invitation comes as former Soviet leader Mikhail Gorbachev warns the US is putting the world on the brink of war.
Mr Gorbachev, the last Soviet leader, denounced the US decision to leave an arms control treaty that helped end the Cold War.
US President Donald Trump, last week, said Washington plans to quit the Intermediate-Range Nuclear Forces (INF) treaty.
Mr Gorbachev and then-US President Ronald Reagan signed the pact, to eliminate all short and intermediate-range land-based nuclear and conventional missiles held by both countries in Europe, in 1987.
But Mr Trump’s announcement to scrap the treaty has been branded a “dire threat to peace” by Mr Gorbachev.
The US stationed land-based nuclear missiles in western Europe in the 1980s – triggering mass protests.
Now some US allies fear Washington might deploy a new generation of missiles in Europe, with Russia doing the same in its exclave of Kaliningrad, once again turning the continent into a potential nuclear battlefield.
If the US made good on its pledge to leave the treaty, Mr Gorbachev said he hoped US allies would refuse to be launchpads for American missiles which Mr Trump has spoken of developing.
Russian President Vladimir Putin said Russia would be forced to target any European countries that agreed to host US missiles.