President Donald Trump and Putin are also expected to meet briefly in Paris on the sidelines of events commemorating the centenary of the end of World War I.
Trump last met with Putin in Helsinki, the Finnish capital, and then issued Putin an invitation to visit Washington in the autumn. The meeting was postponed.
Bolton made the announcement in ex-Soviet Georgia days after meeting Putin and senior security officials in Moscow. Bolton said he gave Putin an invitation to visit next year during his trip to Moscow.
It was not immediately clear if Putin had accepted the invitation. Putin last held a meeting with a U.S. president on American soil in 2015 when he met Barack Obama on the sidelines of a U.N. General Assembly.
Trump has said it is in U.S. interests to establish a solid working relationship with Putin.
Shortly before Bolton met with officials Moscow, Trump announced that the United States would exit the Intermediate-Range Nuclear Forces (INF) treaty with Russia. Washington has said for years that Moscow violated the treaty by deploying a banned missile launch system.
Bolton remained firm on quitting the INF treaty after a 90-minute meeting with Putin.
Only Russia and the United States are bound by the Cold-War era treaty, which banned the possession, production, and testing of short- and mid-range missiles and related equipment. Meanwhile, China, Iran, and North Korea have built up alarming arsenals of the weapons prohibited by the treaty.
Trump said he would be open to a treaty that includes China and other nations.
“We’ll have to develop those weapons, unless Russia comes to us, and China comes to us, and they all come to us and they say, ‘Let’s really get smart and let’s none of us develop those weapons.’” Trump said. “But if Russia is doing it and if China is doing it, and we’re adhering to the agreement, that’s unacceptable.”
Bolton told reporters in Russia that Washington has tried to have other nations join the INF treaty for years with no success.
Days before Bolton’s trip to Moscow, the United State indicted a Russian national for managing the finances of a sophisticated operation aimed at interfering with foreign affairs, including the 2018 midterm elections in the United States. The operation, codenamed “Project Lakhta,” was funded with tens of millions of dollars.
In February, special counsel Robert Mueller, who is investigating Russia’s meddling in the 2016 election, indicted 13 Russian nationals who worked for and financed Project Lakhta, accusing them of interfering with the 2016 presidential election. The 13 were among 19 Russians sanctioned by the United States in March for their roles in election interference and cyberattacks.
In July, Mueller indicted 12 Russian nationals, charging them with hacking the Clinton campaign and the Democratic National Committee. Russians disseminated the emails obtained through the hacks with the intent of interfering in the 2016 election, the indictment alleges.
Russia denies all of the accusations.
None of the indictments against the Russian nationals include any allegation that any American knowingly colluded with Russia.
Bolton told Russian officials that the interference attempts achieved little, but have instead served to undermine the relationship between the United States and Russia.
Reuters contributed to this report.