Putin's spokesman, Dmitry Peskov, would not say whether the congressmen would later meet with Russian President Vladimir Putin.
A US congressional delegation is meeting with senior Russian officials in St. Petersburg amid preparations for a summit between the nations' presidents.
"We are competitors, but we don't necessarily need to be adversaries", said Shelby, a Republican senator from Alabama, in televised comments.
USA intelligence agencies concluded that Putin ordered a hacking-and-propaganda campaign aimed at swaying US voters, and officials later said the Kremlin clearly meant to support Trump.
Peskov was referring to the July 16 Trump-Putin Summit in Helsinki, TASS reported.
The subject came up on Outnumbered today, when the panel talked about how Trump not only wants to meet with Putin one-on-one, and the indications that no Democrats were invited to the meeting in Finland.
"With regard to Trump's negotiating chips, it doesn't really seem like he has any because we've already seen that he is denying that Russian Federation interfered in the 2016 election", she said.
Shelby told Russian Foreign Minister Sergei Lavrov Tuesday that he hoped for an improvement in relations between the United States and the Russian Federation.
Lavrov also congratulated the delegation on the forthcoming US Independence Day and wished them well on hosting the 2026 FIFA World Cup.
Huntsman said the USA needs to hold Russian Federation responsible for "hybrid warfare", which is widely understood to blend conventional and unconventional, regular and irregular, and information and cyber tactics.
"Everyone in our alliance has the same goal, and that is a strong deterrent; an alliance that is unified that can face any threats that any one of our 29 members might face", she said, listing "Russia and the malign activities of Russian Federation, the efforts of Russian Federation to divide our Democratic nations" and INF treaty violations as among those threats.
"We are convinced that inter-parliamentary links are one of the most important factors in bilateral ties", he told reporters.
The head-to-head between the U.S. and Russian leaders will follow a delicate North Atlantic Treaty Organisation summit in Brussels.