The U.S. Senate voted Thursday to end debate on the so-called fast-track trade legislation that is key to concluding the Trans-Pacific Partnership (TPP) negotiations, moving the bill one step closer to final passage.

With a procedure vote of 62 to 38, the Senate agreed to move forward the trade legislation that would grant U.S. President Barack Obama the fast-track authority to negotiate ongoing trade deals.

"I want to thank the bipartisan group of senators who took a big step forward" on the trade agenda, Obama said at the start of a cabinet meeting at the White House, adding that the legislation is "consistent with strong labor standards, strong environmental standards, and access to markets that too often are closed".

The fast-track legislation, formally known as Trade Promotion Authority (TPA), empowers the president to negotiate trade deals and then present them to Congress for up-or-down votes, with no amendments allowed.

If the legislation is passed by the full Congress, it will give U.S. trading partners the confidence they need to put their best offers on the table and help the Obama administration conclude the ongoing TPP free trade talks, which are nearing completion after more than five years of negotiations.

The Senate is expected to have a final vote and pass the legislation before this weekend. But it's unclear whether the House currently has enough votes to approve the bill because some conservatives have opposed giving Obama any authority and only a dozen Democrats have publicly expressed support.

House Ways and Means Committee Chairman Paul Ryan on Tuesday strongly urged lawmakers to back the trade legislation. "I just think it would be a big mistake for our country if we were to fail to do this," Ryan said in an interview with Politico.

"I think this would be a punctuation mark on the declining narrative of America and we should not have our fingerprints, as Republicans, on anything that makes it look like we're in decline," he said.