By Deirdre Walsh and Jeremy Herb

(CNN) -- The House of Representatives overwhelmingly passed a bill giving Congress the power to block any effort by the White House to weaken sanctions on Russia, offering a direct challenge to President Donald Trump's authority.

The vote was 419-3. The legislation moves to the Senate, but it's unclear when the Senate will vote on the measure, which includes new sanctions against Russia, Iran and North Korea. Senate foreign relations committee chairman Bob Corker indicated Monday he may want to make some tweaks to the bill, which was negotiated between the House and Senate after the initial version he drafted sailed through on a 98-2 vote.

"This is a strong, bipartisan bill that will increase the United States' economic and political leverage," Rep. Ed Royce, who heads the House Foreign Affairs Committee, told reporters Tuesday.

The House action came hours after Jared Kushner, the President's son-in-law and senior adviser, wrapped up an interview with the House intelligence committee about the 2016 campaign and allegations that the Trump campaign coordinated with Russian officials to help defeat Hillary Clinton. On Monday he met with staff on the Senate intelligence panel and said afterward that he didn't collude with Russia and didn't know anyone from the campaign who did.

Rep. Eliot Engel, D-New York, who is the top Democrat on the House foreign affairs committee, said he was hearing "a lot of reticence" from some Senators about the bill, which he attributed to "ego" because some in the upper chamber preferred to pass the first version that they crafted. He said he planned to talk to both Corker and Sen. Ben Cardin, the top Democrat on the Senate committee, to urge them to move the legislation forward.

Corker said the Senate might want small tweaks to the North Korean portion of the bill, which was added by the House to the Senate's Russia and Iran sanctions. On Tuesday, Corker didn't specify what the next step will be in the Senate, telling CNN "I guess the House is sending something over and we'll have to figure out what to do with it." He maintained it didn't matter to him if it was a House or Senate bill.

Bipartisan lawmakers from both chambers who worked on the latest bill said they wanted to clear the bill through both chambers and get it to the President's desk before a scheduled summer congressional recess, although that's in doubt with the Senate now focused on health care and the House expected to leave town at the end of the week.

The President has not indicated whether he would sign the bill. In recent days mixed messages emerged from top White House officials, with press secretary Sarah Huckabee Sanders saying the President backed the new bill, but communications director Anthony Scaramucci saying the President needed to weigh in on the issue. Efforts by the Trump Administration to weaken the ability of Congress to push back at the executive branch failed, and instead the revised legislation includes some changes that US companies and European allies wanted to ensure business deals were not affected by new sanctions.

Engel noted there were some provisions in the package that the White House backed, even if it didn't like the Russia piece.

"It's not just a Russia sanctions bill --it's North Korea, it's Iran. I happen to believe all three countries should be sanctioned."

Aides and members of Congress from both parties say if Trump does decide to veto the sanctions bill there will be sufficient votes to override the veto and enact the bill into law.

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