KIEV, Ukraine — Secretary of State Rex W. Tillerson assured Ukraine’s leader on Sunday that the United States would not lift economic sanctions against Russia until it “reverses the actions” that prompted them and restores the country’s “territorial integrity,” appearing to set the same high bar for sanctions relief that the Obama administration did.

Mr. Tillerson’s strongly worded statement, issued at a news conference in Kiev alongside President Petro O. Poroshenko of Ukraine, seemed to insist that Moscow withdraw Russian troops and heavy weapons from the eastern part of Ukraine and return Crimea, the Black Sea territory that Russia annexed in 2014 — though Mr. Tillerson never specifically mentioned that disputed peninsula by name.

His comments came on the same day that President Trump said the issue of sanctions was not discussed at his meeting on Friday with President Vladimir V. Putin of Russia. And Mr. Trump walked into a new controversy over his response to Russia’s efforts to interfere in the 2016 presidential election with his declaration on Twitter that he and Mr. Putin had agreed to create “an impenetrable Cyber Security unit,” suggesting for the first time that the two biggest adversaries in cyberspace would somehow police it together.

Mr. Trump’s tweet came as intelligence officials appeared increasingly convinced that Russian cyberactivity continued well after the election, and that the Russian government was likely behind recent intrusions into business systems at American nuclear power plants.

Mr. Trump said Sunday he had “strongly pressed” Mr. Putin twice during their meeting last week on the sidelines of the Group of 20 summit meeting in Hamburg, Germany, over interference in the election. Mr. Putin’s primary diplomatic objective during their meeting was thought to be the lifting of Western sanctions. Mr. Trump had questioned the value of those sanctions during his 2016 campaign for president, and Mr. Putin may have seen his best opportunity to achieve that goal.

But in a statement posted on Twitter minutes after Mr. Tillerson finished speaking, Mr. Trump wrote that “sanctions were not discussed in my meeting with President Putin,” and added, “Nothing will be done until the Ukrainian & Syrian problems are solved!”

Mr. Tillerson’s statement Sunday in Kiev was more definitive on the issue of sanctions than his boss’s tweet, perhaps a reflection of the political reality the administration faces in Washington, where the Senate voted, 97 to 2, last month to toughen sanctions because of Russia’s continued intervention in eastern Ukraine, Moscow’s attempts to intimidate former Soviet states and the conclusion of American intelligence agencies that Russia had interfered in the 2016 election.

The administration has sought to water down the sanctions bill to give the administration more leeway in dealing with Russia, an effort that was viewed by many Republicans and Democrats as a way to be able to relax sanctions without congressional approval.

It was unclear how the Russians might react to Mr. Tillerson’s comments insisting that Moscow restore Ukraine’s territorial integrity. A few days ago, Mr. Tillerson announced he was appointing a new special envoy, Kurt Volker, an experienced diplomat, to help settle the dispute in Ukraine in part at the request of Mr. Putin. And Russian officials believed they had made progress in Mr. Putin’s meeting with Mr. Trump.

As Mr. Tillerson spoke Sunday, Mr. Volker sat in the front row, and he was to remain in Kiev after Mr. Tillerson departed to discuss how to enforce the largely ignored Minsk accord agreed in 2015 that envisioned a way out of the Ukraine impasse.

During his short news conference in Kiev with Mr. Poroshenko, who took office after one of Mr. Putin’s acolytes was pushed from power, Mr. Tillerson also declined to say whether Mr. Trump, during his meeting with the Russian president, accepted Mr. Putin’s denials that Russia was involved in efforts to influence the 2016 election.

Mr. Tillerson was the only other senior American official in the room during the presidents’ meeting. His Russian counterpart, Sergey V. Lavrov, the Russian foreign minister, told reporters after the meeting in Hamburg that Mr. Trump had been persuaded by Mr. Putin’s arguments.

When pressed on the question, Mr. Tillerson used language he had used Friday night, as the meeting in Hamburg broke up, calling the election hacks the “first topic for discussion.”

“In all candidness, we did not expect an answer other than the one we received,” he said Sunday. “And so I think that was about the way we expected the conversation to go.”

Mr. Trump has frequently expressed doubts about Russia’s involvement in hacking the servers of the Democratic National Committee and compromising the email accounts of prominent Democratic operatives, dismissing the conclusions of American intelligence agencies as politicized in the Obama era.

Mr. Tillerson suggested that the two leaders would never reach a common understanding of what happened last year. “I don’t know if we will ever come to an agreement, obviously with our Russian counterparts on that. I think the important thing is how do we assure that this doesn’t happen again.”

The two sides announced a new effort last week in Hamburg, focused on avoiding interference in elections and curbing cybersabotage.

By Mr. Tillerson’s telling, that effort will start modestly, with discussions about “ a framework under which we might begin to have agreement on how to deal with these very complex issues of cyberthreats, cybersecurity, cyberintrusions.”

Mr. Trump’s tweet seemed to indicate the cooperation would go beyond merely discussions.

To many at the National Security Agency and United States Cybercommand, a “Cyber Security unit” between Russia and the United States as described byMr. Trump would be akin to creating a joint missile-defense unit with the North Koreans. The United States is deeply inside Russian computer networks — for surveillance, and if need be to conduct offensive action — and the same is true about Russian penetration of American networks. It is hard to imagine intelligence services on either side giving that up.