The emails show that, from the earliest months of Mr. Trump’s campaign, some of his associates viewed close ties with Moscow as a political advantage. Those ties are now under investigation by the Justice Department and multiple congressional committees.

American intelligence agencies have concluded that the Russian government interfered with the 2016 presidential election to try to help Mr. Trump. Investigators want to know whether anyone on Mr. Trump’s team was part of that process.

Mr. Sater, a Russian immigrant, said he had lined up financing for the Trump Tower deal with VTB Bank, a Russian bank that was under American sanctions for involvement in Moscow’s efforts to undermine democracy in Ukraine. In another email, Mr. Sater envisioned a ribbon-cutting ceremony in Moscow.

“I will get Putin on this program and we will get Donald elected,” Mr. Sater wrote.

Mr. Sater said he was eager to show video clips to his Russian contacts of instances of Mr. Trump speaking glowingly about Russia, and said he would arrange for Mr. Putin to praise Mr. Trump’s business acumen.

“If he says it we own this election,” Mr. Sater wrote. “Americas most difficult adversary agreeing that Donald is a good guy to negotiate.”