Former U.S. Treasury Secretary Larry Summers warned that failure to move forward in Congress on a 12-nation trade deal spearheaded by the United States will raise questions about American leadership and hurt the country's geopolitical standing.

"It will be a more dangerous world if the United States shows itself again unable to participate in international organizations in a full way and unwilling to support global trade agreements that it initiated," the former economic adviser to President Barack Obama told CNBC.

Amid opposition from Democrats, the House failed to pass a bill that would have cleared the way for Obama to negotiate a sweeping trade deal with Pacific countries.

House Democrats were instrumental in defeating the measure, known as Trade Adjustment Assistance, which provides aid to U.S. workers who lose their jobs as a result of foreign trade.

While Democrats support the program, they oppose major parts of the Trans-Pacific Partnership (TPP), which faces opposition from labor unions.

"If we want to be relied upon, if we want people to be interested in our initiatives, if we want to remain a substantial and trusted presence in Asia, a negotiation that we launched three years ago and that we've driven has to be a negotiation that the United States can carry through on," he said.

"If the United States is not able to carry through, that will raise questions about the capacity for presidential leadership both for the remainder of this presidential term and going forward," he said. "No other country in the world wants to be in the position of negotiating first with the president, and then with a Congress whose behavior can't be predicted."

Summers has warned that “the repudiation of the TPP would neuter the U.S. presidency for the next 19 months.”

Meanwhile, President Barack Obama and his legislative allies scrambled Monday to try to revive his severely wounded trade agenda, although Democrats and Republicans alike said all options have serious hurdles, the Associated Press reported.

Republican Rep. Kevin McCarthy of California told reporters "there are many different options" to revive the trade package the House derailed last week.

He said a new vote could come as early as this week, but Republican leaders first must survey the political and legislative landscapes.

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