Washington(CNN) Secretary of State Rex Tillerson said Friday that US sanctions against Russia will remain in place until Moscow "reverses the actions" it has taken in Ukraine.

The comments are notable given President Donald Trump's at-times reluctance to criticize Russia over its actions in Crimea, though he did declare last month that the territory was "taken" by Russia. As a candidate, Trump hinted he might recognize Russia's annexation of Crimea, and sources have previously told CNN that Ukraine-related sanctions were on the table for review as part of Trump's interest in pursuing warmer ties with Moscow.

"American and NATO support for Ukraine remains steadfast. As we have repeated at every ministerial and summit since Russia launched its campaign of aggression against Ukraine, NATO allies stand firm in our support of Ukraine's sovereignty and territorial integrity," Tillerson said at a NATO meeting at the organization's headquarters in Brussels. "We do not, and will not, accept Russian efforts to change the borders of territory of Ukraine."

He added, "We will continue to hold Russia accountable to its Minsk commitments. The United States sanctions will remain until Moscow reverses the actions that triggered our sanctions."

At his confirmation hearings in January, Tillerson called Russia's claims on Crimea "illegitimate." His comments on Friday also echo those made by US Ambassador to the United Nations Nikki Haley, when she told the UN Security Council last month that US sanctions against Russia would remain in place until it withdraws from Crimea.

Earlier Friday, Tillerson and Defense Secretary James Mattis criticized Russian actions in overseas comments aimed at reassuring US allies.

Mattis, appearing with his British counterpart in London, also called out the Putin regime for "mucking around" in other people's elections -- a particularly notable claim coming at a time when federal and congressional investigators are probing alleged Russian meddling in the US elections last November.

"We look to engaging with Russia on a political or diplomatic level, but right now, Russia is choosing to be a strategic competitor," Mattis said during a news conference with Michael Fallon, the UK defense secretary. "We are going to have to carve out diplomatically some kind of maneuver room here, assuming Russia can change its behavior and act in accordance with international norms and international law."

He also said "Russian activity" in Afghanistan "gives us concern," though he stopped short of saying the Putin government was arming the Taliban.

In response to Mattis, Alexey Pushkov, a senior Russian lawmaker, tweeted, "New US administration sounds just like the old one — Mattis is indistinguishable from (former Defense Secretary Ash) Carter, Tillerson is talking about 'Russian aggression.' (Barack) Obama and (Hillary) Clinton must be happy."

Tillerson is in Brussels to reinforce US commitment to NATO -- an organization Trump has repeatedly criticized -- and referred to the alliance as "the bedrock for transatlantic security."

"We understand that a threat against one of us is a threat against all of us, and we will respond accordingly. We will uphold the agreements we have made to defend our allies," he added.

The Trump administration's top diplomat, however, reiterated on Friday Trump's call for members to increase their financial contributions to the organization.

"Our goal should be to agree at the May leaders meeting that by the end of the year, all allies will have either met the pledge guidelines or will have developed plans that clearly articulate how, with annual milestone progress commitments, the pledge will be fulfilled," Tillerson told the ministers.

Hopes for a thawing relationship fading

But Trump's hopes of striking a grand bargain with Russia are fading, two administration officials told CNN Thursday.

According to one senior administration official, this isn't necessarily because Trump's view of Putin has evolved. But Trump believes in the current atmosphere -- with so much media scrutiny and ongoing probes into Trump-Russia ties and election meddling -- that it won't be possible to "make a deal," as the President himself has framed it, the officials said.

One of the White House officials said the President was particularly "frustrated" in a meeting in the Oval Office with newly minted national security adviser H.R. McMaster and other top officials in the wake of Russia's February cruise missile deployment -- an apparent treaty violation.

This official said that with each violation from Russia, the President views it as that much harder to make amends. The President is not closing the door on engaging with Russia on a variety of issues -- including Syria, Ukraine and combating ISIS -- but the administration is not optimistic at the moment.