The Times said the document was based on notes taken from inside the Oval Office.
Former FBI Director James Comey will testify publicly before the Senate intelligence committee, committee leaders announced Friday.
Another government official who spoke to The Times said Trump was using a "negotiating tactic" with Lavrov when he explained the "pressure" he faced.
"By grandstanding and politicising the investigation into Russia's actions, James Comey created unnecessary pressure on our ability to engage and negotiate with Russia", White House Press Secretary Sean Spicer said. "By grandstanding and politicizing the investigation into Russia's actions, James Comey created unnecessary pressure on our ability to engage and negotiate with Russian Federation", he said.
That does absolutely nothing to help Trump with the pervasive speculation that he fired Comey because of the investigation into his Russian ties.
"I'm not under investigation", he added.
The latest developments come at an inopportune for Trump who just embarked on a nine-day worldwide trip, his first trip overseas since assuming office. The trip is seen by some analysts as a chance for Trump to hit reset after more than a week of intense controversy in Washington in the wake of the Comey firing.
For more of Liasson's summary from this week of USA political news, use the audio player above.
In a statement Mr Spicer said Mr Comey's pursuit of the probe had harmed Mr Trump's ability to deal with Russian Federation over issues including Syria and Ukraine.
The individual was described by the paper as a senior adviser who is close to the president, but the Post's sources would not further identify them.
Mr. Trump said: "I'm not under investigation".
Capping days of political drama in Washington, Mueller's appointment came as Trump fends off a stunning series of allegations including claims he shared U.S. secrets with Russian officials in the Oval Office.
Democratic Senator Claire McCaskill said Rosenstein told senators that he knew Comey would be fired before he wrote his letter accusing him of missteps as Federal Bureau of Investigation director, including his handling of an election-year probe into Clinton's use of a private email server while she was secretary of state. Deputy Attorney General Rod Rosenstein reportedly informed members of Congress of this on Friday, according to McClatchy.
Mr Trump also thanked Israel's leaders for being committed to achieving peace between Israelis and Palestinians. Mr Trump also called upon countries around the world to work together to end the humanitarian crisis in Syria.
A seal lion has been captured on video grabbing a little girl by her dress and pulling her into the water to her family's horror. Fujiwara claims people were feeding the sea lion breadcrumbs, something Steveston Harbour Authority GM Bob Baziuk warns against.
Ruby Rose slammed Katy Perry as a bully, but stepped back from making further vicious comments about the singer's new single. She's not referring to anyone specific, so the song is most definitely about someone specific (*cough* Taylor *cough*).
Across its investment strategies, infrastructure investing has been one of Blackstone's most successful and active areas. General Electric also announced that the firm sealed a deal for $15 billion worth of projects.
The king of the Netherlands has revealed he has been living a secret double life as a co-pilot for a commercial airline. For the King flying is a hobby, in which he sees the opportunity to "disengage and concentrate on something else".
The Red Devils face Dutch giants Ajax knowing a win will give them another trophy and a place in next season's Champions League . We have a good relationship and I will always say nothing ever happened, we didn't have an argument or anything like that.
She recently broke Aretha Franklin's record for most songs placed on the Billboard Hot 100 chart by a female artist. Accepting the night's biggest award, Top Artist, Drake brought up a huge entourage that include Lil Wayne, Nick.
Trump visited the Western Wall without any Israeli government officials by his side despite requests from Israeli officials. Trump also planned to visit the Holocaust memorial Yad Vashem and the Western Wall, an important key Jewish holy site.
Nashville had tied the score 1-1 on Wilson's power-play goal, his second goal of the playoffs, at 19:19 of the second period. The Ducks will also be shorthanded, with forward Rickard Rakell not making the trip to Nashville after missing Game 5.
Nepal has cleared 371 mountaineers to climb Mt Everest during the current season ending this month. He fell sick on his way down from the summit on Saturday and did not make it to the nearest camp.
Social media joins hunt for Manchester concert victims
They said in a statement: "Words can not express our sorrow for the victims and families harmed in this senseless attack". Sobbing, Charlotte Campbell took to global airwaves, pleading for anyone who may have seen Olivia to please come forward.
IT sector to create 25-30 lakh jobs by 2025: Prasad
The Corporation will hire both from government and the private sector. "NeGD (National e-governance division)", he said. Prasad said the Centre had roped in consulting firm McKinsey to help draw a roadmap to achieve this target.
Trump seeks coalition to 'stamp out extremism'
The commander-in-chief stepped away from his anti-Muslim rhetoric by calling Islam "one of the world's great faiths". He was addressing the heads of 50 Muslim majority countries during his first speech on foreign soil.
Rent-to-own scheme one of key planks of Lib Dem manifesto
THE LIBERAL DEMOCRATS are promising another Brexit vote and the legalisation of cannabis as part of their election manifesto . Under the Conservative government's current plans for a new funding formula, schools in Birmingham will lose £20 million.
ACC baseball teams head to Louisville for conference tourney
The Tigers have earned the fifth seed in the tournament and will play in Pool D with fourth seed Virginia and ninth seed Duke. The Cards first game in the ACC Tournament this week is Thursday at 7 p.m. against Notre Dame at Louisville Slugger Field.
Kriti upset with Sushant Singh Rajput again?
The 26-year-old actress will next feature in Ashwiny Iyer Tiwari's Bareilly Ki Barfi , co-starring Ayushmann Khurrana. The film is based on the theme of incarnation and revolves around Shiv and Saira's love story which transcends time.