(CNN) Ahead of President Donald Trump's first face-to-face encounter with Russian President Vladimir Putin next week at the G20 summit, Congress appeared to get Russia sanctions legislation back on track Thursday.

But the lingering dispute — which wasn't resolved until two weeks after the Senate overwhelmingly passed the Russia sanctions bill 98-2 — has Democrats accusing House Republicans of stalling the bill on the White House's behalf so that Trump wouldn't sign it into law ahead of the Putin meeting.

The Senate passed technical changes to the bill by unanimous consent on Thursday, kicking the measure back to the House with minor tweaks that House leaders said were necessary to comply with the Constitution.

House leaders insisted the changes were necessary because of a constitutional requirement that bills generating revenue originate in the House. Democrats, however, said the so-called "blue slip" issue could have been easily and quickly dealt with in the House.

It's unclear how quickly House Republican leaders will move to bring the measure up for a vote, but any action at this point would position final congressional votes after the President's meeting with Putin next week.

The blame game over the bill dragged out over the course of the week, and the House was preparing to leave for its weeklong recess with a final vote series Thursday afternoon by the time the Senate had approved the new language.

"We should have passed it already, and letting it go into the break without taking care of what needs to be taken care of worries me a bit," said New York Rep. Eliot Engel, the top Democrat on the House Foreign Affairs Committee. "(House Speaker Paul Ryan) told me that he agreed the bill should be moved, but the devil is in the details."

One House committee chairman is already working to put the brakes on the Russia sanctions bill that the Senate tweaked and passed again Thursday.

"We should not move it straight to the floor," House Rules Committee Chairman Pete Sessions, R-Texas, told CNN. He has expressed his concerns about some provisions in the bill that he says are "huge problems to companies in Dallas, Texas, that I represent" and argued it could put them at a competitive disadvantage.

"The bill bypasses jurisdictional elements and puts an ability for any Member of Congress to become engaged in data and information that today is considered proprietary and private that is material to people who do overseas business," the Texas Republican said. He said it's was either specifically written that way, or those in the Senate who drafted it made a mistake.

Asked why Senate Republicans didn't raise objections to these issues, Sessions said, "you'll have to ask them."

Pressed on Democrats' charge that those holding up the bill to do the White House's bidding on Russia, Sessions replied, "I am concerned about companies from Dallas, Texas that I continue to support."

The Senate's bill, which includes sanctions on both Iran and Russia, is a rebuke of Trump and his favorable comments about the Kremlin. In addition to establishing new sanctions against Russia, the bill would create a new congressional review process for Congress to block the Executive Branch if it tries to ease sanctions on Moscow.

Ryan has insisted that the dispute was over the constitutional issue, and Republicans have pushed back on the notion they were delaying the bill for the White House.

"They wrote the bill incorrectly," Ryan told reporters Thursday. "They did not pass it correctly — they violated constitutional protocols."

The White House says it's still reviewing the legislation and has not taken a position, though press secretary Sean Spicer and Secretary of State Rex Tillerson have both raised concerns about Congress eroding the administration's authority to determine sanctions.

"I think our main concern overall with sanctions is how will the Congress craft them, and any potential erosion of the executive branch's authority to implement them," Spicer said last week.

Before the bill passed two weeks ago, Tillerson testified before a Senate panel that he was concerned about Congress taking actions that could interfere with the administration's attempts to improve relations with Russia.

"What I wouldn't want to do is close the channels off," Tillerson said.

Treasury Secretary Steve Mnuchin, pressed whether the President would sign the bill and whether his department would enforce new sanctions, argued the administration was already implementing existing measures.

"Notwithstanding anything Congress passes, I can assure you, this administration and the Treasury Department will use sanctions to the maximum amount available by law. We don't need Congress to tell us to put on more. We're going to do more whether they tell us or not," Mnuchin said, not directly addressing the new legislation.

Democrats have been wary that the House is trying to water down the bill or bury it with procedural hurdles, and both House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer called for the House to immediately pass the measure on Thursday before Congress left for recess.

"We wanted to send a message to Mr. Putin: If you interfere with our democratic institutions, you will be punished," Schumer said. "It's important for Speaker Ryan to act on this legislation before July 4 recess."

Senate Foreign Relations Committee Chairman Bob Corker said he did not think that House Republicans were stalling, but he grew frustrated with the dispute between House Republicans and Senate Democrats, calling it "total silliness" on Wednesday before the issue was resolved.

On Thursday, Corker wasn't concerned that the bill would slip into next month, so long as it was ultimately signed into law intact.

"You all are in a tizzy about a minor issue that should have been handled in an hour," Corker told reporters. "This is a technical issue that changes in no way the context of the bill."