"You can thank Congress, the same people that can't even give us HCare!" the president said, referencing the failure of the Senate to pass legislation overhauling the Affordable Care Act, a long-term GOP priority and marquee Trump campaign promise.
The president's assessment came a day after he begrudgingly signed legislation, passed by overwhelming majorities in the House and Senate, that imposes new sanctions on Russia and places restrictions on his ability to roll back measures already in place.
In a statement Wednesday, Trump criticized the bill he signed as "seriously flawed," arguing that it encroaches on his powers as president. Trump also said that he had "built a great company worth many billions of dollars" and asserted that he "can make far better deals with foreign countries than Congress."
Lawmakers from both parties pushed back against Trump's tweet Thursday. Those included Sen. Bob Corker, R-Tenn., chairman of the Foreign Relations Committee, who pinned blame for the current U.S.-Russia relationship "solely" on Russian leader Vladimir Putin.
"I know there's some frustration. I get it," Corker said, speaking of the sanctions bill. "We acted in the country's national interest in doing this. Putin through his actions is the one who has taken this relationship back to levels we haven't seen since 1991."
Those activities, Corker said, include "an affront to the American people" by meddling in last year's presidential election.
Lawmakers' solidarity in tying Trump's hands on Russian sanctions reflects a deepening concern about the White House's posture toward Moscow, which critics have characterized as naive.
The new Russia sanctions expand on measures taken by the Obama administration to punish the Kremlin for its alleged efforts to interfere in the 2016 presidential election. But Trump has continued to cast doubt that Russia alone was responsible, and he has called the investigations of the matter by Congress and by a special counsel a "witch hunt."
Russia this week reacted to Congress's passage of the sanctions bill - as well as the earlier Obama-imposed measures - by announcing that it would order the U.S. Embassy there to reduce its staff by 755 people and seize U.S. diplomatic properties.
Russian Prime Minister Dmitry Medvedev criticized Trump on Wednesday for signing the bill.
"The Trump administration has shown its total weakness by handing over executive power to Congress in the most humiliating way," he tweeted.
Trump has sought to build a relationship with Putin, repeatedly asserting that the United States and Russia have shared interests.
During the Group of 20 summit in Germany last month, the two leaders met for a much-publicized meeting that ran more than two hours - far longer than scheduled - and chatted informally for up to an additional hour later the same day during a dinner for G-20 leaders.
Thursday's tweet comes at a time of fraying relationships between Trump and Senate Republicans in particular. GOP senators have sought to distance themselves from the president, who has belittled them as looking like "fools" and tried to strong-arm their agenda and browbeat them into changing a venerated rule to make it easier to ram through legislation along party lines.
Among those speaking out about Trump on Thursday were Sen. Jeff Flake, R-Ariz., who read the president's tweet off a reporter's phone.
"Huh. Well. It is what it is," Flake said. Asked whether he agreed with the president, Flake said: "Congress' fault? I don't think so."
His Republican colleague from Arizona, Sen. John McCain, responded to Trump on Twitter with a different party to blame: "You can thank Putin for attacking our democracy, invading neighbors & threatening our allies," McCain wrote.
Democrats were also critical of the president's tweet Thursday.
"That shows a continuing lack of understanding by the president of what happened," said Sen. Mark R. Warner, D-Va., who earlier tweeted that the blame for the deteriorating U.S.-Russian relationship rests with Putin.
Michael F. Bennet, D-Colo., meanwhile, offered this succinct response to Trump's tweet: "That is ridiculous."
Abby Phillip and Sean Sullivan contributed to this report.