WASHINGTON — A senior Russian official who claimed to be acting at the behest of President Vladimir V. Putin of Russia tried in May 2016 to arrange a meeting between Mr. Putin and Donald J. Trump, according to several people familiar with the matter.

The news of this reached the Trump campaign in a very circuitous way. An advocate for Christian causes emailed campaign aides saying that Alexander Torshin, the deputy governor of the Russian central bank who has been linked both to Russia’s security services and organized crime, had proposed a meeting between Mr. Putin and Mr. Trump. The subject line of the email, turned over to Senate investigators, read, “Russian backdoor overture and dinner invite,” according to one person who has seen the message.

The proposal made its way to the senior levels of the Trump campaign before Jared Kushner, the president’s son-in-law and a top campaign aide, sent a message to top campaign officials rejecting it, according to two people who have seen Mr. Kushner’s message.

Though the meeting never happened, Mr. Torshin’s request is the latest example of how the Russian government intensified its effort to contact and influence the Trump campaign last year as Mr. Trump was closing in on the Republican presidential nomination. It came just weeks after a self-described intermediary for the Russian government told a Trump campaign aide, George Papadopoulos, that the Russians had “dirt” on Mr. Trump’s rival, Hillary Clinton, in the form of “thousands of emails.”