WASHINGTON — In case anyone had doubt, the White House wanted it known on Thursday that it was President Vladimir V. Putin of Russia who asked to meet with President Obama, not the other way around.

Mr. Putin was not just eager for a meeting, said Josh Earnest, the White House press secretary, but in fact “desperate” for one.

The emphasis on who wanted to meet more underscored the sensitivities and risks of the meeting, which the White House officially announced on Thursday. Mr. Obama has not seen Mr. Putin in nearly a year, and the two have not had a formal sit-down meeting in more than two years, before Russia annexed Crimea and intervened in eastern Ukraine.

“It is fair for you to say that based on the repeated requests we’ve seen from the Russians, that they are quite interested in having a conversation with President Obama,” Mr. Earnest said. Ultimately, Mr. Obama decided “that it was worth it at this point to engage with President Putin in a face-to-face meeting to see if the interests of the United States could be advanced.”