For his first three years as the head of the C.I.A., William J. Burns was relentlessly focused on tripling the agency’s resources devoted to understanding China, and on countering Russia and its mysterious partnerships with Iran and North Korea.

But in the last 16 months of his tenure, the diplomat-turned-spy was plunged back into his old life.

Over four decades at the State Department, Mr. Burns came to be regarded as the master of creating “the back channel” — the title of his memoir — the invisible, essential outreach to allies and enemies alike.

As the Israel-Hamas war threatened to pull the Middle East into a larger conflagration, President Biden asked Mr. Burns to swim in that back channel once again, blending his intelligence role with his experience as a Middle East negotiator to help find a way to a cease-fire and the release of hostages held in Gaza.

Soon he was, by his own account, “on the phone every day” with David Barnea, the head of Israel’s foreign spy agency, and Prime Minister Mohammed bin Abdulrahman Al Thani of Qatar, the link to Hamas, searching for an opening, for some leverage to bring about a truce and maybe a new Middle East.

The distinction between a diplomatic negotiator and an intelligence operative is vague in the region, and Mr. Burns’s arrivals and departures could be stealthy. “It makes it easier to come and go,” he said in his office on the 7th floor of the C.I.A., with its memorabilia of the agency’s operations and successes, and a framed map of the Russian plan to move in on Ukraine.