WASHINGTON — In the early days of the Trump administration, national security officials began exploring ways to free Austin Tice, an American journalist and a former Marine officer believed to be held by the Syrian government. His case has frustrated investigators and diplomats since he disappeared while on assignment nearly five years ago.

White House officials decided, because of the delicacy of the situation, to set up a back channel. Given the deteriorated relations between the United States and Syria, options were limited. So in early February, Mike Pompeo, the C.I.A. director, spoke on the phone with Ali Mamlouk, the head of Syria’s National Security Bureau intelligence service, a man accused of human rights abuses during the country’s civil war and slapped with sanctions by the United States. The call was the highest-level contact between the governments in years.

Though Mr. Pompeo’s discussion with Mr. Mamlouk prompted further communications that renewed hope that Mr. Tice would be freed, the operation fizzled out after the Syrian government’s nerve gas attack in rebel-held northern Syria in April and the American missile strike in response, according to several former United States officials who spoke on the condition of anonymity because the efforts to free Mr. Tice remain secret.

The plight of Americans held hostage by reclusive foreign governments has received renewed attention since the death on Monday of Otto F. Warmbier, a 22-year-old college student from Ohio who was arrested in North Korea in January 2016. Many of the most difficult cases involve nations — like Syria — that have no diplomatic relations with the United States, giving American officials little leverage to negotiate. Outreach to Syria by President Trump’s administration shows how far it has been willing to go to secure the release of Americans held abroad.