U.S. Secretary of State Mike Pompeo told CNBC's Hadley Gamble on Saturday that such criticism — including from members of the previous administration — fails to recognize what Trump's team has done, or the missteps of past presidents.
"Boy, that's crazy talk. That's absolutely crazy talk. And I've heard it — I've heard it from the previous administration. They say, 'Oh, we're not tough on Russia.' I only wish they would have stopped the election interference," Pompeo said, referring to Kremlin meddling in the 2016 U.S. elections.
"I only wish they would have put global Magnitsky on some of the bad actors in Russia in the way this administration" has, he said. "I only wish they hadn't gutted the defense budget to the great benefit of Vladimir Putin."
The Magnitsky Act is an Obama-era law that lets the United States punish individual human rights offenders.
Trump's administration has "put real money into our Defense Department," Pompeo said, characterizing the American military build up as inherently problematic for Russia.
"Vladimir Putin can't possibly think that's a good thing for him," he said.
Notably, Trump has both sought to increase the U.S. military budget as well as suggested he would like to work with the Russian president to cut down on the "crazy" arms race.
Still, Pompeo said his boss has been as tough as any president on Russia.
"The actions that this administration takes I would put up against any in terms of our seriousness in pushing back on Russia and raising costs for them," the secretary of state said.
Washington still hopes, however, to find common ground with Moscow, Pompeo said, pointing to Syria and Afghanistan as places where the U.S. and Russia can work together. The topic of Venezuela, he suggested, is more complex.
Political analyst Ian Bremmer, founder of risk consultancy Eurasia Group, backed up Pompeo's assertion on the White House's approach toward Russia.
"I do agree with Pompeo's point that it's crazy talk to say the Trump administration isn't tough on Russia," he told CNBC, citing a former U.S. ambassador to Russia. "Mike McFaul — Obama's own ambassador to Russia — admitted to me a few weeks ago that Trump administration policy towards Russia has been harder line than Obama's."
Indeed, some of the toughest sanctions in years have fallen on Russia's elite under the Trump administration. Sanctions imposed over Russia's invasion of Crimea in 2014 have not been lifted, Trump approved the sale of lethal weapons to Ukraine — something Obama did not do — and he's ordered missiles fired at Syrian military sites, openly targeting strategic operations and allies of Russia.
"But Pompeo avoids mentioning that Trump personally takes every opportunity to put a friendly face towards the Russians, and President Putin in particular, in marked contrast to the way he engages with, say, most European allies," Bremmer added.
Critics of the president point to his delays in implementing congressional sanctions and frequent praise of Putin's leadership, as well as apparent reluctance to act on Moscow's cyber aggression and dismissive attitude toward U.S. intelligence conclusions that the Kremlin meddled in the U.S. election in favor of Trump.
In general, the secretary of state said he has a responsibility to try to make progress with Putin's regime.
"There are places that we'll have a value set that is radically different, that we'll have different views. In those places we're going to protect America's interests," he said. "But in those places where we can find common ground or an overlapping interest, it's completely appropriate, and, indeed, my duty and a necessity, that we work together."
—CNBC's Natasha Turak and Emma Graham contributed to this article.