House Speaker John A. Boehner (R-Ohio), left, walks through the halls of Congress before a series of critical trade votes at the Capitol on Friday. (Mark Wilson/Getty Images)

President Obama claimed a modest victory Tuesday with approval of a rule giving his congressional allies until the end of July to reconsider the stalled package of trade legislation that Democrats sabotaged last week.

Setting aside initial plans to formally hold a second vote on the initiative, House Speaker John A. Boehner (R-Ohio) pushed for the new vote to give him until the end of July to revive the existing legislation. After a morning meeting with his GOP rank and file, Boehner told reporters Tuesday that the decision came after “several discussions” with Obama a day earlier.

In the 236-to-189 vote, Obama relied heavily on Republicans to extend the lifeline on the existing trade legislation.

The vote came as the pro-trade coalition of mostly Republicans and several dozen Democrats in the House and Senate began considering other options toward getting the legislation to the president’s desk. A trio of West Wing officials met with members of the New Democrat Coalition, a group of House Democrats that is largely supportive of expanded global trade, according to lawmakers and aides.

Exiting a huddle of Senate Republican leaders, Sen. John Cornyn (R-Tex.), the majority whip, said that their team had already been in contact with White House officials to figure out other paths toward passage of the entire collection of trade-related bills in the next few weeks.

Later, Senate Majority Leader Mitch McConnell (R-Ky.) told reporters he was willing to carve out more time to consider a newly crafted version of the legislation, after having devoted two weeks to the original draft in May before it was approved in a bipartisan vote.

The leading option late Tuesday was to separate the carefully crafted package of trade-related bills into several pieces. The Senate could amend a House-approved bill dealing with promoting trade with African nations to attach a popular worker training program, which House Democrats have successfully blocked, at the same time the House passes a stand-alone bill granting Obama “fast track” authority for trade deals and send that to the Senate.

House Majority Leader Kevin McCarthy (R-Calif.) said no final decision has been made on that plan, which would still require more House Democrats to come on board to approve the combined ­African-trade and worker-training legislation. McCarthy said he was “pretty sure” enough Democrats would stick with Republicans to approve the trade authority bill.

Despite the talk of a new direction, White House spokesman Josh Earnest called the move to buy more time on the existing trade package a “prudent one.”

The move will “give members of the House and Senate additional time to consider the path forward,” he said. “In this case, we are pleased that Democrats and Republicans appear to be working together to try to find this path.”

Earnest said Obama has not spoken with House Minority Leader Nancy Pelosi (D-Calif.) on trade since House Democrats derailed his agenda last week.

The failed vote Friday, after an unusually personal set of pleas for Democratic support from Obama, exposed the deepening divisions among the party along the lines of pro-business Democrats and the collection of unions and liberal activists who have gained more influence in recent years espousing an anti-Wall Street agenda.

Republicans, including arch conservatives who have openly feuded with their leadership, acknowledged that they were taking some enjoyment in watching the Democratic infighting. Rep. Jim Jordan (R-Ohio), a leader of the Freedom Caucus, said several dozen fellow conservatives decided to reverse their earlier opposition to the rules of the trade debate and support Boehner on Tuesday because the measure would give Democrats more time to fight within their party.

“There’s nothing wrong with letting the Democrats continue to fight with each other,” Jordan said. “I think it would be much better for leadership to just talk to us and work with us.”

Some House Democrats — fewer than 1 in 4 supported the president last week — cast a poor light on the idea of continued backroom negotiations. Rep. Xavier Becerra ­(D-Calif.), the No. 4 Democratic leader, said the move to extend a possible revote until as late as July 30 was “shady stuff” and “underhanded” and held the potential for procedural skulduggery.

“We would all hope that whatever is done is done in the plain sight of the day and not in some backroom deal,” he said.

The House hit its logjam Friday despite the centerpiece of the legislation, the fast-track Trade Promotion Authority, winning approval on a 219-to-211 vote.

It would set up expedited procedures for Congress to vote on any future trade deals, particularly the 12-nation Trans-Pacific Partnership that Obama is close to finalizing and says will be critical to establishing U.S. global economic leadership.

Labor unions and their liberal allies in Congress strongly oppose the TPP deal, arguing its benefits for multinational corporations will not help increase wages for U.S. workers and will lead to greater job losses. In order to stall Obama’s trade agenda, rank-and-file Democrats rebelled against a companion bill that would fund job-skills training for workers displaced by the competition of the global economy.

Democrats were expected to provide the vast majority of support for that legislation, as they have for two decades, but they decided to block the bill in order to stall the entire trade agenda — the internal House rules required each piece of the package to win majority support, or else it would remain stuck.

For now, Boehner and Obama agreed to try to buy more time on the original piece of legislation, in case there is a major change of heart among Democrats to support the Trade Adjustment Assistance job-skills program.

Still, Boehner acknowledged that he gave a browbeating address to his rank-and-file Republicans on Tuesday morning in advance of the vote that would give him the additional six weeks. The “rules votes” are traditionally considered parliamentary matters and pass on partisan lines, but several dozen conservatives have been defying leadership of late and opposing these votes.

“Frankly, I made it pretty clear that I’m not happy,” Boehner told reporters.

Becerra suggested that the new rule giving additional time for the vote was pointless. Democrats would remain unwilling to support aid to displaced workers, he said, as long as its passage would pave the way to the approval of fast-track authority.

But moments later, the Democratic whip, Rep. Steny H. Hoyer (Md.), suggested that votes remained in play — perhaps by tying trade measures to a pending Highway Trust Fund reauthorization or another popular infrastructure bill.

“I certainly think there would be a number of Democrats that would look at that as possibly affecting their votes,” he said.

But Hoyer said it was “probably questionable” that a combined trade and infrastructure measure could gain passage by the end of July, when Congress leaves town for a month-long recess.

David Nakamura and Kelsey Snell contributed to this report.