President Trump's team on Tuesday imposed sanctions on a pair of Russian government officials and several Russian-backed separatists over the ongoing conflict in eastern Ukraine, a move designed to needle Russian President Vladimir Putin's regime.

"These designations will maintain pressure on Russia to work toward a diplomatic solution," Treasury Secretary Steven Mnuchin said Tuesday. "This administration is committed to a diplomatic process that guarantees Ukrainian sovereignty, and there should be no sanctions relief until Russia meets its obligations under the Minsk agreements."

The Minsk agreements, named for the city in which they were signed, are a pair of ceasefire deals designed to strike a balance between the Ukrainian government's desire to regain control of its territory and Putin's desire to have greater influence over parts of Ukraine that are populated by ethnic Russians. Mnuchin's announcement, which coincided with a visit to the White House by Ukrainian President Petro Poroshenko, also reiterated the Trump administration's refusal to recognize the annexation of Crimea, a strategically-significant Ukrainian peninsula that Putin seized in 2014.

"These steps are consistent with the U.S. commitment to seek a diplomatic resolution to the crisis in Ukraine and to facilitate Crimea's return to Ukraine," the Treasury Department emphasized. "U.S. sanctions on Russia related to the situation in eastern Ukraine will remain in place until Russia fully honors its obligations under the Minsk Agreements. U.S. sanctions related to Crimea will not be lifted until Russia ends its occupation of the peninsula."

The Minsk deals have failed to end the violence despite repeated rounds of talks, as Russia has accused Ukraine of failing to give greater political autonomy to the separatist regions, while the Russian-backed fighters have attacked Ukrainian forces and tried to expand the territory under their control.

In addition to targeting separatist leaders in Ukraine, Treasury took aim at a Russian government official who voted in favor of the annexation of Crimea, Alexander Babakov, and members of his staff. Babakov is top Russian government liaison to "organizations representing Russians living abroad," making him a key player in Russia's argument that they have a responsibility to represent ethnic Russians in other countries.

An overwhelming majority of senators voted in favor of legislation imposing new sanctions on Russia over its support for Ukrainian separatists, among other things. But while the Trump administration has pledged not to lift the sanctions previously imposed by then-President Barack Obama, Secretary of State Rex Tillerson signaled the administration does not want to be handed a mandate from Congress.

"I would urge Congress to ensure any legislation allows the president to have the flexibility to adjust sanctions to meet the needs of what is always an evolving diplomatic situation," Tillerson told the House Foreign Affairs Committee at the opening of a hearing on the State Department's budget request. "Essentially, we would ask for the flexibility to turn the heat up when we need to, but also to ensure that we have the ability to maintain a constructive dialogue."