Laying bare deep and dangerous divisions on Syria and other issues, President Donald Trump declared that U.S. relations with Russia “may be at an all-time low.” His top diplomat offered a similarly grim assessment from the other side of the globe after meeting with Russian President Vladimir Putin in Moscow.

“Right now we’re not getting along with Russia at all,” Mr. Trump said flatly during a White House news conference on Wednesday. It was stark evidence that the president is moving ever further from his campaign promises to establish better ties with Moscow.

Only weeks ago, it appeared that Mr. Trump, who praised Mr. Putin throughout the U.S. election campaign, was poised for a potentially historic rapprochement with Russia. But any such expectations have crashed into reality amid the nasty back-and-forth over Syria and ongoing U.S. investigations into Russia’s alleged interference in America’s U.S. presidential election.

“It’d be a fantastic thing if we got along with Putin and if we got along with Russia,” Mr. Trump said. But he clearly wasn’t counting on it.

“That could happen, and it may not happen,” he said. “It may be just the opposite.”

Not long before Mr. Trump spoke in Washington, Secretary of State Rex Tillerson struck a similar tone after an almost two-hour meeting with Mr. Putin, saying the two countries had reached a “low point” in relations.

Mr. Trump, who last week ordered airstrikes on a Syrian air base in retaliation for a chemical weapons attack, was asked on Wednesday if Syria could have launched the attack without Russia’s knowledge. Mr. Trump said it was “certainly possible” though “probably unlikely.”

The newly hardened view of Moscow comes as the president has tried to shake suspicions about the motives behind his campaign calls for warmer relations. As the FBI and multiple congressional committees investigate possible collusion between Russia and Trump’s campaign, the President and his aides can now point to his hard-line stance on Syrian President Bashar Assad as evidence he’s willing to stand up to Mr. Putin.

More than 80 people were killed in what the U.S. has described as a nerve gas attack that Assad’s forces undoubtedly carried out. Russia says rebels were responsible for whatever chemical agent was used, which the Trump administration calls a disinformation campaign.

Not long before Mr. Trump spoke, Russia vetoed a Western-backed U.N. resolution that would have condemned the chemical weapons attack and demanded a speedy investigation.

The dim view of U.S.—Russian ties from both Mr. Trump and Mr. Tillerson reflected the former Cold War foes’ inability to forge better relations, as Mr. Trump until recently has advocated.

Allegations of collusion between Russian officials and Mr. Trump campaign associates also have weakened Mr. Trump’s ability to make concessions to Russia on any issue, lest he be accused of rewarding bad behavior. Russia wants the U.S. to eliminate sanctions on Moscow related to its 2014 annexation of Ukraine’s Crimea region and support for pro-Russian separatists in eastern Ukraine.

Until the chemical attack, the Trump administration had sought to step back from the U.S. position that Mr. Assad should leave power. But Mr. Tillerson repeated the administration’s new belief that “the reign of the Assad family is coming to an end.”

Beyond Syria, Russia’s alleged meddling in the U.S. presidential election also hovered over what was the first face-to-face encounter between Mr. Putin and any Trump administration Cabinet member.

Russian Foreign Minister Sergey Lavrov blasted U.S. claims that it has “irrefutable evidence” of election interference.

“We have not seen a single fact, or even a hint of facts,” he said. “I do not know who saw them. No one showed us anything, no one said anything, although we repeatedly asked to produce the details on which these unfounded accusations lie.”

Still, Mr. Tillerson sought to stress the positives from his meetings. He said working groups would be established to improve U.S.—Russian ties and identify problems. He said the two sides would also discuss disagreements on Syria and how to end the country’s six-year civil war.

But such hopes appeared optimistic as the diplomats outlined their sharply diverging views on Syria. Mr. Tillerson said Syria’s government had committed more than 50 attacks using chlorine or other chemical weapons over the duration of the conflict. And he suggested that possible war crimes charges could be levied against the Syrian leader. Russia has never publicly acknowledged any such attacks by Assad’s forces and has tried for the past 18 months to help him expand his authority in Syria.

The civil war is separate from the U.S.-led effort against the Islamic State group in the north of the country.

While the most immediate U.S.—Russian dispute concerns culpability for the chemical weapons, broader disagreements over everything from Ukraine to Russia’s support for once-fringe candidates in European elections are among other sore points.

Mr. Tillerson was greeted frostily in the Russian capital as Mr. Lavrov began their meeting on Wednesday by demanding to know America’s “real intentions.”

“We have seen very alarming actions recently with an unlawful attack against Syria,” Mr. Lavrov said, referring to the 59 Tomahawk missiles Mr. Trump ordered to be launched at an air base to punish Mr. Assad for using chemical weapons. “We consider it of utmost importance to prevent the risks of replay of similar action in the future.”

Mr. Trump and others have indeed threatened similar action. But in a Fox Business Network interview, the U.S. President said he wouldn’t intervene militarily against Assad unless the Syrian leader resorts to using weapons of mass destruction again. “Are we going to get involved with Syria? No,” Mr. Trump said. But, he added, “I see them using gas ... we have to do something.”