Ahead of the chat Russia's security chief said he had high hopes for the call between Russian President Vladimir Putin and President Donald Trump.
Trump said Friday that having Russian Federation as an ally "would be an asset".
TRUMP: Well, I hear a call was set up, Steve, and we'll see what happens.
Trump then spoke by phone from with German Chancellor Angela Merkel.
In a statement on Friday, the Arizona Republican pledged to work in the Senate "to codify sanctions against Russian Federation into law" if Trump moves to lift them.
He kept quiet about which most crucial issues Putin and Trump might discuss.
Despite that earlier move on the multilateral TPP, Trump and Abe also "committed to deepen the bilateral trade and investment relationship" on Saturday, according to the White House. "As far as the sanctions, it's very early to be talking about that, but we look to have a great relationship with all countries ideally", he said.
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In her high-profile foreign policy speech on the eve of her meeting with Mr Trump, Mrs May said: "When it comes to Russian Federation, as so often it is wise to turn to the example of President Reagan who - during negotiations with his opposite number Mikhail Gorbachev - used to abide by the adage "trust but verify".
The series of calls follows a week of dramatic action from Trump's new administration, mostly initiated through executive orders that have sent signals both at home and overseas that the new president aims to amke dramatic changes to longstanding US policies.
"I know that Mr. Trump is considered a master of deal-making, but President Putin also knows how to make deals, and always in Russia's interests", Lavrov said.
"I believe the U.S. Senate should take pro-active steps to codify the sanctions against Russian Federation into law to ensure we live up to our commitments to our allies and uphold longstanding American values and ideals", Portman wrote in a statement.
The Saturday chat marked the first known time that Trump and Putin have talked since Trump's January 20 inauguration.
Mr Putin's spokesman Dmitry Peskov told reporters that the conversation is scheduled for Saturday. He stressed that it is an initial contact, saying that "one should hardly expect that this phone call will involve substantive discussions across the whole range of issues".
May announced she had gotten Trump to commit to remaining in North Atlantic Treaty Organisation, and congratulated him on a "stunning" election victory.
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That's what great players do. "It should be good football to watch, and I'm pretty sure both Ben and Brady will be into it". The reason the Patriots won last week was not so much because of Brady but because Houston was completely inept on offense.