WASHINGTON — Lawmakers from both parties on Sunday expressed opposition to President Trump’s plans to host Vladimir Putin in Washington this year, with even some of the administration’s Republican allies conceding that last week’s encounter with the Russian president did not go well.

Trump, for his part, plunged ahead on Twitter with efforts to portray the Helsinki summit as a triumph and to impugn the motives and methods of U.S. law enforcement agencies looking into links between his 2016 presidential campaign and Russia as the Kremlin worked to subvert the election in his favor.

And the president was back to calling the Russia matter “all a big hoax” after repeatedly clarifying last week — under pressure from advisors and leading Republicans — that he does believe the U.S. intelligence agencies’ findings of Russian interference. Trump ignited a firestorm of bipartisan fury after the July 16 summit by accepting Putin’s denials of interference during their news conference in Helsinki, Finland.

His series of combative tweets began early Sunday when the president declared that the summit had been “GREAT.” He also asserted, without evidence, that his campaign had been illegally spied upon by the FBI. Late in the day, as he returned to Washington from a weekend at his Bedminster, N.J., golf club, Trump tweeted his complaint that the Russia reports were a Democratic hoax.

On Sunday’s television talk shows, the closest thing to a staunch defense of Trump’s meeting with Putin came from a former aide, Tom Bossert, who had been an advisor for homeland security. Yet even as Bossert called the talks “productive,” he pushed back at Russia’s emerging narrative that the two leaders had privately made agreements that would run counter to previously stated U.S. policy.

“They didn’t agree on anything, unlike what’s been reported by, apparently by, the Russian government in a way to mislead us,” Bossert said in an interview on ABC’s “This Week.”

Bossert conditioned his assessment on the fact that the White House has failed to offer an accounting, even to senior U.S. intelligence officials, of what occurred in the closed-door meeting between the two leaders. That is a highly unusual decision that has drawn broad expressions of concern, as did Trump’s insistence on meeting alone with Putin in the first place, without the usual senior advisors and note takers. Critics had warned that the format risked enabling Russia to put its own spin on the session.

Several senior Democrats said Trump’s public show of skepticism of U.S. intelligence conclusions about Russian election interference — while he stood next to Putin — suggested that the Russian leader, a onetime spymaster, had some kind of hold over him.

Trump grudgingly walked back one of those remarks after returning to Washington, but then muddied the waters again — first by suggesting unspecified “others” might have interfered in the U.S. election as well, an assertion unsupported by intelligence, and then by answering “no” when he was asked the next day whether Russia is continuing to “target” the United States generally.

The White House then said that too was a misunderstanding.

“For whatever reason, this president acts like he’s compromised,” Rep. Adam B. Schiff of Burbank, the ranking Democrat on the House Intelligence Committee, said on ABC. “There is simply no other way to explain why he would side with this Kremlin, former KGB officer, rather than his own intelligence agencies.”

Sen. Robert Menendez (D-N.J.) said on “Fox News Sunday” that Trump “seems to want to be chummy” with Putin rather than to defend U.S. interests. That, he said, boded ill for another high-profile meeting with the Russian leader.

“Now we’re going to give him a red-carpet treatment and invite him to Washington,” Menendez said. “To me, that’s beyond comprehension.”

Some Republicans chimed in with similar criticism, even including Rep. Trey Gowdy of South Carolina, who has championed Trump’s cause in criticizing the wide-ranging investigation by special counsel Robert S. Mueller III.

Gowdy, also on Fox, suggested Trump’s invitation to Putin — which caught even senior administration figures like Dan Coats, the director of national intelligence, unawares — was unwise.

“The fact that we have to talk to you [Russia] about Syria or other matters is very different from issuing an invitation,” said Gowdy, who heads the House Oversight Committee. “Those should be reserved for, I think, our allies.”

A fellow South Carolina Republican, Sen. Lindsey Graham, also said Trump had not done enough to stand up to Putin, and warned that such acquiescence would invite stepped-up Russian aggression.

“Just have sanctions that can fall on Russia like a hammer,” Graham said on CBS’ “Face the Nation.”

“Do you meet with this guy from a position of weakness?” asked Graham, as if directly addressing Trump about the Russian leader. “If you were really tough with Putin, he would not be doing what he is doing.”

Despite such publicly aired misgivings about Trump’s dealings with Putin, Republicans largely continued to support, or at least condone, the president’s insistence that the Mueller investigation is a “witch hunt.”

Putin acknowledged in Helsinki that he had wanted Trump to win but again denied that any interference had taken place — a denial that Trump seemed to accept, over unanimous U.S. intelligence findings to the contrary.

Gowdy, who has spearheaded an effort among House Republicans to discredit elements of the Mueller inquiry, said heavily redacted documents released late Saturday by the Justice Department — which described the FBI’s suspicions and evidence that former Trump campaign advisor Carter Page might have been collaborating with Moscow — demonstrated government overreach and bad faith.

But another Republican, Sen. Marco Rubio of Florida, interviewed on CNN’s “State of the Union,” said he believed the warrants to monitor Page were justified.

Rubio also took issue with Trump’s Sunday tweet claiming his campaign was illicitly surveilled at the behest of Democrats. Trump had written on Twitter: “Looking more & more like the Trump Campaign for President was illegally being spied upon.” He said, referring to Hillary Clinton: “Ask her how that worked out.”

“I don’t believe that them looking into Carter Page means they were spying on the campaign,” Rubio said. For U.S. intelligence officials, he said, Page “was a guy that was on their screen even before the campaign.”

Page, interviewed on the same program, offered contradictory accounts of his entanglements with Russian officials.

“I’ve never been an agent of a foreign power, by any stretch of the imagination,” he said. But pressed by interviewer Jake Tapper, he admitted he had worked as an informal advisor to the Russian government — part of a pattern of activity that attracted the attention of the FBI.

laura.king@latimes.com

Twitter: @laurakingLAT