Mr. Cohen and his account will be subjected to deep scrutiny by Republicans, who have already begun to hammer away with questions about his past business dealings and credibility. They plan to use Wednesday’s hearing to paint Mr. Cohen as self-centered and untrustworthy — a man who ran afoul of the law, including by lying to Congress once before, and then once he was caught, sought to spin lies about his former boss to reduce his time in prison.

Mr. Cohen will address his own past lies head-on and plans to use documents to try to bolster certain claims. He plans to draw a picture of Mr. Trump using the type of nonspecific directives more often associated with organized crime bosses than with American presidents.

“In conversations we had during the campaign, at the same time I was actively negotiating in Russia for him, he would look me in the eye and tell me there’s no business in Russia and then go out and lie to the American people by saying the same thing,” Mr. Cohen plans to say. “In his way, he was telling me to lie.”

He will add: “Mr. Trump did not directly tell me to lie to Congress. That’s not how he operates.”

Mr. Cohen also plans to say that Mr. Trump’s personal lawyers approved his testimony, suggesting that they signed off on him telling a false version of events to the House and Senate Intelligence Committees. Mr. Cohen is meeting with both committees again in private this week in part to correct those earlier false statements.

“Mr. Trump knew of and directed the Trump Moscow negotiations throughout the campaign and lied about it,” Mr. Cohen will say. “He lied about it because he never expected to win the election. He also lied about it because he stood to make hundreds of millions of dollars on the Moscow real estate project.”