Putin's plane touched down in Helsinki 30 minutes later than planned, pushing back the start of his one-on-one talks with Trump Monday.
In an interview with CBS at a golf club in Scotland, after wrapping up his three-day visit to Britain, Trump was quoted by CNN saying: "I think we have a lot of foes".
A second, expanded bilateral meeting with presidential aides followed the first session.
Commentators on popular Sunday night talk show "Vecher" or "Evening" said Putin goes into Monday's summit in Helsinki as the stronger figure, notably coming off his hosting of the World Cup.
This all comes just several days after Deputy Attorney General Rod Rosenstein announced 12 Russian intelligence officers were being indicted on charges related to the hacking of the Democratic National Committee as part of the special counsel Robert Mueller's investigation into Russian election interference.
Director of National Intelligence Dan Coats on Monday directly challenged comments by President Trump, saying the USA intelligence community has been "clear in our assessments of Russian meddling in the 2016 election".
Asked whether Mrs May had urged Mr Trump to raise the Salisbury attack with Mr Putin, the PM's spokesman said: "The US position has been set out very clearly by the president with relation to the Skripals".
The first one he named was the European Union, traditionally a close ally to the U.S.
While Mr Trump was eager for a made-for-TV spectacle that will dominate headlines like his sit-down with North Korean leader Kim Jong Un last month, the Kremlin's primary mission was simply to have the summit happen. You know the Russians take the position - you can like it or not like it - that their Constitution forbids them to extradite Russian citizens'. Huntsman said the summit must go on because Russian engagement is needed to solve some global issues. And when another user tweeted "holy f****n s**t" following the news conference, Hayden responded, "I agree".
Special counsel Robert Mueller is investigating possible links between Trump campaign associates and Russian Federation as part of his probe into Moscow's attempts to interfere in the 2016 election.
Russian Ambassador Jon Huntsman said recently that the meeting itself is a deliverable.
The United States has no extradition treaty with Moscow and can not compel Russian Federation to hand over citizens.
"I would not have said it the way John (Brennan) said it. John can say it the way he wants to say it". "I will be asking that question again".
The Human Rights Campaign placed banners on Finland's Presidential Palace on Sunday which target Putin for the treatment of Chechnya's LGBTQ population, and Greenpeace placed two banners atop the city's Kallio church calling on both leaders to "Warm Our Hearts, Not Our Planet".