By Siobhan Hughes 

WASHINGTON--The Senate on Friday passed major trade legislation that would pave the way for President Barack Obama's signature Pacific trade deal, marking a victory for the Obama administration and Republican leaders in Congress and sending the bill toward an uncertain fate in the House.

Lawmakers defeated a controversial amendment on currency manipulation that drew a veto threat from the White House and then moved the bill steadily through to a final vote just one day after a revolt among some Democrats nearly derailed the bill, a major priority for Mr. Obama.

The Senate voted 62-37 to approve so-called fast track, which would help conclude the Trans-Pacific Partnership with Japan and 10 other countries and ensure that the Pacific deal and others would get an up-or-down vote in Congress without amendments.

The Pacific agreement, which officials could finish soon if the House also approves fast-track, is set to lower tariffs and other barriers at the border and institute commercial rules of the road designed to spur flows of goods, services and finance in a dozen countries comprising some 40% of global economic output.

The Senate passage of fast track, also known as trade promotion authority, is a win for Mr. Obama and Treasury Secretary Jack Lew, who made personal calls to clear roadblocks in recent days and discourage senators from approving language that would mandate enforceable rules against currency manipulation, opposed by trading partners.

"I want to thank senators of both parties for sticking up for American workers by supporting smart trade and strong enforcement, and I encourage the House of Representatives to follow suit," Mr. Obama said in a statement.

The bill's passage also vindicated a strategy of Senate Majority Leader Mitch McConnell (R., Ky.), who gambled that he would be able to push fast track through before the Memorial Day recess, while allowing at least some debate and amendments as he had promised. It was unclear late Friday if the plan would allow for renewing a highway program and a national-security program, without cutting short the recess.

"The House will take up this measure, and Republicans will do our part, but ultimately success will require Democrats putting politics aside and doing what's best for the country," House Speaker John Boehner said in a statement.

Only 14 Democrats voted for fast track, and opponents complained that Mr. McConnell didn't allow sufficient time for debate on the measure. Backed by labor groups, most Democrats oppose fast track and the Pacific deal, saying it would move some jobs overseas and do little to help the working class.

Friday's vote marked a defeat for Sen. Elizabeth Warren (D., Mass.), who clashed with Mr. Obama in recent weeks, criticizing the secrecy of TPP negotiations and arguing that fast track could be used by a future president to erode regulations favored by Democrats, including rules for Wall Street.

Lawmakers voted down her amendment that would prevent trade deals from getting an expedited vote if they include an established but controversial arbitration system that allows investors to challenge foreign governments.

The most difficult fight Friday came over an amendment backed by two senators from auto states--Sen. Rob Portman (R., Ohio) and Sen. Debbie Stabenow (D., Mich.)--that would press the administration to crack down on overseas currency manipulation through enforceable rules in the TPP. Mr. Lew called the legislation a "poison pill" for the trade talks, but Mr. Portman said it was a "vitamin."

The amendment was rejected, 48-51, but Mr. Portman, a former U.S. trade representative, said he would "keep up the fight" on inserting currency rules favored by Detroit auto makers worried they will lose tariff advantages in the TPP. "There's an opportunity in the House," he said.

"We look forward to continuing to work with lawmakers to address this critical issue as TPA moves through the legislative process," said Ziad Ojakli, vice president for government and community relations at Ford Motor Co.

Instead of the Portman-Stabenow amendment, the Senate approved a less binding currency amendment backed by the architects of fast track legislation, Sen. Orrin Hatch (R., Utah) and Sen. Ron Wyden (D., Ore.).

Enforceable currency rules are a priority for the top Democrat on the House committee that oversees trade, Rep. Sander Levin of Michigan, who also backs measures to ensure Detroit's cars make inroads in the Japanese market.

Sen. Chuck Schumer (D., N.Y.), who opposes Mr. Obama's trade policy, warned that the House may need enforceable currency rules to pass fast track. He has backed a separate set of binding currency rules in a customs bill Congress is considering.

All but a dozen or so House Democrats oppose fast track, and a broad group of conservatives is wary about supporting policies that could put pressure on businesses in their districts or grant additional authority to Mr. Obama. Others are concerned about the commercial rules Mr. Obama is touting in the TPP, or the religious restrictions and foreign policies of trading partners.

Republican leaders had hoped the House would also consider fast track before the one-week recess, since liberal and conservative grass-roots opponents of Mr. Obama's trade policy are expected to put pressure on lawmakers back home.

"That's always a concern--individuals go back to their districts and they're subject to misinformation that's put out there," said Rep. Charles Boustany (R., La.), who's helping build GOP support for fast track.

Labor groups say that too little information about the TPP is public and have vowed to help defeat the legislation in the House.

"This is a sad day," United Steelworkers President Leo Gerard said in a statement. "At election time, voters will remember who was on their side and who voted to sell them out."

Write to Siobhan Hughes at siobhan.hughes@wsj.com