“The best play for us is him landing in a third country,” Monaco said, according to an official who met with her at the White House. The official, who like other current and former officials interviewed for this article discussed internal deliberations on the condition of anonymity, added, “We were hoping he was going to be stupid enough to get on some kind of airplane, and then have an ally say: ‘You’re in our airspace. Land.’ ”

U.S. officials thought they saw such an opening on July 2 when Bolivian President Evo Morales, who expressed support for Snowden, left Moscow aboard his presidential aircraft. The decision to divert that plane ended in embarrassment when it was searched in Vienna and Snowden was not aboard.

A year later, Snowden appears to have moved further beyond U.S. reach. His expiring asylum status in Russia is expected to be extended this summer. Negotiations between his attorneys and the Justice Department about a possible deal to secure his return have been dormant for months.

U.S. officials offer conflicting accounts of how much they know about Snowden’s situation in Russia.