HOUSTON — Exxon Mobil is pursuing a waiver from Treasury Department sanctions on Russia to drill in the Black Sea in a venture with Rosneft, the Russian state oil company, a former State Department official said on Wednesday. An oil industry official confirmed the account.

The waiver application was made under the Obama administration, the officials said, speaking on condition of anonymity, and the company has not dropped the proposal.

The proposal is now before the Trump administration at a delicate time in Russian-American relations, with rising tensions over the war in Syria and a looming congressional inquiry into reports of Russian efforts to influence the United States presidential election.

The appeal did not come up during Senate confirmation hearings for Secretary of State Rex W. Tillerson, who was Exxon Mobil’s chief executive before his nomination by President Trump and was known to have a strong working relationship with President Vladimir V. Putin of Russia. At the time, Mr. Tillerson and other company officials said they had not lobbied against the sanctions, which were imposed on Russia in response to its military intervention in Ukraine.