WASHINGTON — A 12-nation Pacific trade agreement cleared a crucial test in the U.S. Senate Thursday, giving a resounding thumbs-up to legislation that holds the key to President Barack Obama’s diplomatic pivot to Asia.

Just two days after Democrats defied Obama to block debate on the “fast-track” trade negotiating authority that he needs to complete the Trans-Pacific Partnership trade deal, the Senate voted 65 to 33 to move ahead with considering the measure.

On this second try, 13 of 44 Democrats supported the legislation after they won a separate vote on a bill punishing countries that unfairly manipulate their currencies to keep their exports cheap, and following a renewed round of personal lobbying by Obama.

Republicans voted in lock-step to give supporters of the legislation more than the 60 votes needed to proceed in the 100-member Senate.

Under fast-track, Congress can approve or reject trade deals, such as the Trans-Pacific Partnership deal, but it cannot amend the contents of the pact, a key part of Obama’s strategy to counter China’s rising economic and diplomatic clout in Asia.

In the previous two days, Obama talked with almost a dozen senators and met with others at the White House, a senior administration official said late Wednesday.

The Senate is expected to debate amendments to the bill next week. One likely amendment would impose tough rules against currency manipulation in trade deals, which the Obama administration opposes.

While 60 votes were needed to get past the procedural hurdle, only a simple majority of the 100-member Senate will be needed for passage, although additional procedural votes are possible.

The bill must also pass the House of Representatives, where a tougher fight is expected. Trade is a hot-button issue with many Democrats in the United States, as labor unions and environmentalists — two of their important political supporters — are actively trying to kill fast-track.

Senators earlier on Thursday approved a separate bill with rules against currency cheats, which the White House has also warned against, although it sees the real danger in planned amendments to graft sanctions against currency cheats onto trade deals such as the Trans-Pacific Partnership.

The Trans-Pacific Partnership would create a free trade zone covering 40 percent of the world economy, making it the biggest trade deal since the North American Free Trade Agreement liberalized trade between the United States, Canada and Mexico.

More than two decades later, that pact is blamed by many on the left for factory closures and job losses and has soured sentiment toward the Trans-Pacific Partnership.

Negotiations on the Trans-Pacific Partnership are nearly complete, but trading partners have said they want to see the legislation enacted before finalizing the pact — a task the administration wants to complete this year.

Left-wing Democrats want tougher controls on foreign labor and environmental standards, which they see as necessary to create a level playing field.

Some conservative Republicans, meanwhile, could end up voting against fast-track next week because they do not want to give Obama any new powers.

Obama’s aggressive defense of fast-track has put him at odds with the left wing of the Democratic Party, pitting him against Sen. Elizabeth Warren, a leading liberal voice.

The Senate also passed a bill extending duty-free access to U.S. markets for African and other developing nations.