The congressional probe comes after a January Washington Post report that said Trump has gone to great lengths to hide the details of his communications with Putin from senior administration officials, including one instance where he seized the notes of his interpreter at a private meeting with Putin in Hamburg, Germany, in 2017.
House Judiciary Committee Chairman Jerrold Nadler told CNN that nobody should draw conclusions just because some people affiliated with Trump's administration and businesses were not included on the initial list.
Trump has vehemently denied all allegations of collusion with Russian Federation during his 2016 presidential campaign and has repeatedly railed against Mueller's investigation into the matter as a "hoax".
Cohen was sentenced last December to three years in prison for crimes including campaign finance violations over hush payments before the 2016 election to women who said they had sex with Trump.
The Judiciary Committee is investigating possible obstruction of justice, corruption and abuse of power.
"The Democrats cannot stand the loss, they could not stand losing in 2016".
President Trump dismissed Mr Nadler's probe as a "political hoax", but added: "I co-operate all the time with everybody".
Bernie Sanders launches 2020 presidential bid
Bernie Sanders , I-Vt., hugs his wife Jane after he finished speaking Saturday, March 2, 2019, in the Brooklyn borough of NY . Kamala Harris (D-CA), Cory Booker (D-NJ), and most notably Elizabeth Warren (D-MA), who share similar sensibilities.
Large-scale investigations led by the FBI, Congress, and special counsel Robert Mueller haven't yielded any evidence of wrongdoing by Trump.
Democrats, he charged, are motivated only by resentment that he won the White House.
More than five House committees are now investigating alleged attempts by Russian Federation to meddle in the 2016 election campaign, the president's tax returns and potential conflicts of interest involving Mr Trump's family. Trump's campaign spokeswoman, Kayleigh McEnany, accused Democrats of stopping "at nothing, including destroying the lives and reputations of many innocent Americans who only have sought to serve their country honourably, but who hold different political views than their own".
The request asks American Media for "all documents that relate to the purchase of rights for any narrative, personal account, documentation, recording, or photograph (including but not limited to materials colloquially referred to as "catch and kill") concerning Donald Trump from June 2015 to the present". Liberal members of the Democratic caucus who are adamant about pushing impeachment were fired up by the event; in that context, the document requests might be an effort by House leadership to keep restive elements under control.
She said White House lawyers and "relevant White House officials" would review the Judiciary Committee's demand for documents and "respond at the appropriate time".
Trump's exclamation mark - and capital letter - laden outbursts indicated a rising temperature in a White House under assault from multiple directions.
White House Press Secretary Sarah Huckabee Sanders called the House investigation a "disgraceful and abusive. fishing expedition". Former White House chief of staff John Kelly and former White House counsel Don McGahn also are likely targets, he said.