Trump arrived here on Sunday night from Scotland after wrapping up his United Kingdom visit.
A second, expanded bilateral meeting with presidential aides followed the first session.
Trump set expectations for the summit low, telling CBS News, "I don't expect anything". I think having meetings with the president of China was a very good thing.
Trump did not explicitly say he believed Putin on the subject of election interference but did say the Russian leader's denials were "extremely powerful".
US Ambassador to Russia Jon Huntsman also downplayed expectations, saying the two leaders were merely going to have a "conversation" rather than a "summit".
Editor-in-chief Kaius Nieme also explained that the banners are intended as a display of support for "colleagues who have to fight in ever toughening circumstances on a daily basis both in the US and Russian Federation", noting that both countries sit pretty far down on the 2018 World Press Freedom Index.
The summit comes just days after special counsel Robert Mueller issued indictments on 12 Russian spies for their alleged interference in the 2016 US presidential election.
They brushed off new indictments of Russians accused of hacking the 2016 US presidential campaign.
Former Defense Secretary Chuck Hagel said Trump "failed America today", but stopped short of calling the President's behavior "treasonous".
The first one he named was the European Union, traditionally a close ally to the U.S.
During last week's North Atlantic Treaty Organisation summit in Brussels, Trump repeatedly criticized members for failing to spend more on defense and openly questioned the alliance's goal. Huntsman said the summit must go on because Russian engagement is needed to solve some global issues.
"The US doesn't have and won't have a better ally than the EU".
He also criticised special counsel Robert Mueller's investigation stemming from the alleged election meddling by Russian Federation in the 2016 USA presidential election, calling it a "rigged witch hunt".
Mrs May's spokesman said that the U.S. president had already made clear, not least through his expulsion of 60 Russian diplomats, that he shares the PM's judgment that Moscow was responsible for the nerve agent attack on Sergei and Yulia Skripal that last week claimed the life of Dawn Sturgess.
He has denied any collusion by his campaign with the Russians.
Trump's remarks at the news conference brought swift condemnation from Democrats and Republicans alike.
It was the second time since the dozen Russian intelligence officers were indicted Friday that Trump described the Mueller probe as a "rigged witch hunt".
The 2018 Russia-United States summit will focus on improving ties between the two countries.
"I think it's important to the country that he stay where he is", Lugar said. "I can't tell you what's going to happen, but I can tell you what I'll be asking for".