"Until we know what happened at that two hour meeting in Helsinki, the president should have no more one-on-one interactions with Putin. In the US, in Russia, or anywhere else," Schumer said on Thursday.
White House spokeswoman Sarah Huckabee Sanders said earlier in the day that Trump asked National Security Adviser John Bolton to invite Putin to visit the United States in the fall, and the consultations on the meeting have already started.
Trump and Putin met for the first official summit in Helsinki, Finland on July 16.
The two presidents had a one-on-one private conversation and then held a joint press conference during which they announced that they have discussed Syria, Ukraine, and alleged Russia's meddling in the 2016 US presidential election.
Trump clarified his remarks the day after he arrived back from the trip. The US president said he misspoke about the fact that Russia would not meddle in the US democratic process. Trump said he remains confident in the US intelligence community's assessment of Russia's role in the November 8 election.