WASHINGTON — The House Intelligence Committee released a redacted Democratic memorandum on Saturday countering Republican claims that top F.B.I. and Justice Department officials had abused their powers in spying on a former Trump campaign aide.

The document was intended by Democrats to offer a point-by-point refutation of what it called the “transparent” attempt by President Trump’s allies on the committee to undermine the congressional and special counsel investigations into Russia’s meddling in the 2016 presidential election and possible coordination with the Trump campaign.

But the dueling accounts reflected an extraordinary struggle on the committee to try to shape public perceptions of the credibility of the nation’s top law enforcement agencies. For weeks, instead of focusing its full energy on investigating an attack on the American democratic system, the committee has been pulled into a furious effort by Mr. Trump and his allies to sow doubts about the integrity of the special counsel inquiry and the agencies conducting it.

The Democratic memo amounted to a forceful rebuttal to the president’s portrayal of the Russia inquiry as a “witch hunt” being perpetrated by politically biased leaders of the F.B.I. and the Justice Department.