In response to questions, Mr. Papadopoulos’s lawyers declined to provide a statement.

Before the end of the month, Mr. Mifsud had arranged a meeting at a London cafe between Mr. Papadopoulos and Olga Polonskaya, a young woman from St. Petersburg whom he falsely described as Mr. Putin’s niece. Although Ms. Polonskaya told The Times in a text message that her English skills are poor, her emails to Mr. Papadopoulos were largely fluent. “We are all very excited by the possibility of a good relationship with Mr. Trump,” Ms. Polonskaya wrote in one message.

More important, Mr. Mifsud connected Mr. Papadopoulos to Ivan Timofeev, a program director for the prestigious Valdai Discussion Club, a gathering of academics that meets annually with Mr. Putin. The two men corresponded for months about how to connect the Russian government and the campaign. Records suggest that Mr. Timofeev, who has been described by Mr. Mueller’s team as an intermediary for the Russian Foreign Ministry, discussed the matter with the ministry’s former leader, Igor S. Ivanov, who is widely viewed in the United States as one of Russia’s elder statesmen.

When Mr. Trump’s foreign policy team gathered for the first time at the end of March in Washington, Mr. Papadopoulos said he had the contacts to set up a meeting between Mr. Trump and Mr. Putin. Mr. Trump listened intently but apparently deferred to Jeff Sessions, then a senator from Alabama and head of the campaign’s foreign policy team, according to participants in the meeting.

Mr. Sessions, now the attorney general, initially did not reveal that discussion to Congress, because, he has said, he did not recall it. More recently, he said he pushed back against Mr. Papadopoulos’s proposal, at least partly because he did not want someone so unqualified to represent the campaign on such a sensitive matter.

If the campaign wanted Mr. Papadopoulos to stand down, previously undisclosed emails obtained by The Times show that he either did not get the message or failed to heed it. He continued for months to try to arrange some kind of meeting with Russian representatives, keeping senior campaign advisers abreast of his efforts. Mr. Clovis ultimately encouraged him and another foreign policy adviser to travel to Moscow, but neither went because the campaign would not cover the cost.

Mr. Papadopoulos was trusted enough to edit the outline of Mr. Trump’s first major foreign policy speech on April 27, an address in which the candidate said it was possible to improve relations with Russia. Mr. Papadopoulos flagged the speech to his newfound Russia contacts, telling Mr. Timofeev that it should be taken as “the signal to meet.”