WASHINGTON — When the Trump administration announced last month that it was lifting sanctions against a trio of companies controlled by an influential Russian oligarch, it cast the move as tough on Russia and on the oligarch, arguing that he had to make painful concessions to get the sanctions lifted.

But a binding confidential document signed by both sides suggests that the agreement the administration negotiated with the companies controlled by the oligarch, Oleg V. Deripaska, may have been less punitive than advertised.

The deal contains provisions that free him from hundreds of millions of dollars in debt while leaving him and his allies with majority ownership of his most important company, the document shows.

With the special counsel’s investigation into Russia’s role in the 2016 election continuing to shadow President Trump, the administration’s decision to lift sanctions on Mr. Deripaska’s companies has become a political flash point. House Democrats won widespread Republican support last week for their efforts to block the sanctions relief deal. Democratic hopes of blocking the administration’s decision have been stifled by the Republican-controlled Senate.