Senator John Cornyn of Texas, the chamber’s No. 2 Republican, defended President Trump, saying, “We know the president’s got an unconventional style, but so far it seems to be working for him.”

WASHINGTON — As President Trump and his advisers take aim at some of America’s closest allies amid tense disputes over trade, congressional Republicans largely stood by the president on Monday, insisting they were not worried about a possible deterioration of relations with the West.

A weekend of bellicose remarks by the president and his aides — including unusually personal attacks against the Canadian prime minister — left some Republican commentators fuming that congressional leaders were unwilling to speak out in defense of the world order that has defined American foreign policy for three-quarters of a century.

However, Senate Republican leaders did stand up to Mr. Trump in one respect: They have agreed to amend a defense policy bill by tacking on a bipartisan measure to restore penalties on the Chinese telecommunications giant ZTE. The Trump administration announced a deal last week to ease sanctions on the firm, which American intelligence officials regard as a national security threat.

But a separate, much more sweeping bipartisan measure that would limit Mr. Trump’s authority to impose tariffs on allies such as Canada, Mexico and the European Union remained in limbo on Monday, as Senate Republican leaders appeared to be maneuvering to block it. Senator John Cornyn of Texas, the chamber’s No. 2 Republican, told reporters he did not think the limits were necessary.

“The chance of getting a presidential signature on this at this point, I don’t think is good,” Mr. Cornyn said, adding, “I don’t think having that fight right now is necessary.”

The back and forth over the Senate trade measures came as Washington was grappling with just how far Mr. Trump had strayed from the traditional Republican embrace of free trade. At a tense weekend meeting of leaders of the Group of 7 nations, the president criticized tariffs imposed on American goods as “ridiculous and unacceptable” and vowed to retaliate with additional levies beyond the steel and aluminum tariffs already in place.

When Prime Minister Justin Trudeau of Canada pushed back, Mr. Trump accused him of being “weak” and “dishonest.” The White House trade adviser, Peter Navarro, followed up on Sunday by declaring on television that there is a “special place in hell” for foreign leaders who cross the president. Mr. Trump weighed in again on Sunday night, with a fresh…