On Saturday, the White House said the new memo fails to answer serious questions.
White House press secretary Sarah Huckabee Sanders said questions raised by a memo released earlier by Republicans on the House intelligence committee cover the use of partisan opposition research from one candidate as the basis for asking a federal court to approve surveillance of a former associate of a rival candidate.
Sanders said the Democratic memo is "politically driven."
She said nothing in the memo counters the fact, as the president has been insisting, that neither he nor his campaign ever colluded with a foreign power during the 2016 election.
The top Democrat on the intelligence panel, California Rep. Adam Schiff, had criticized Trump for treating the two documents differently. But he still pledged to work with the FBI on redactions.
Trump has said the GOP memo "vindicates" him in the ongoing Russia investigation led by special counsel Robert Mueller. But congressional Democrats and Republicans, including House Speaker Paul Ryan and Rep. Trey Gowdy of South Carolina, who helped draft the GOP memo, have said it shouldn't be used to undermine the special counsel.
Partisan disagreements on the intelligence committee have escalated over the last year as Democrats have charged that Republicans aren't taking the panel's investigation into Russian election meddling seriously enough. They say House Intelligence Committee Chairman Devin Nunes' memo is designed as a distraction from the probe, which is looking into whether Trump's campaign was in any way connected to the Russian interference.
The warrant at issue in the Republican memo was obtained under the Foreign Intelligence Surveillance Act, or FISA. The main allegation in the GOP document was that the FBI and Justice Department didn't tell the court enough about Steele's anti-Trump bias or that his work was funded in part by Hillary Clinton's campaign and the Democratic National Committee. They argued that the reliance on Steele's material amounted to an improper politicization of the government's surveillance powers.
Democrats have countered that the GOP memo was inaccurate and a misleading collection of "cherry-picked" details. They noted that federal law enforcement officials had informed the court about the political origins of Steele's work and that some of the former spy's information was corroborated by the FBI.
—CNBC contributed to this report.