WASHINGTON — Senator Rand Paul, Republican of Kentucky, said on Sunday that he would support a resolution that would overturn President Trump’s declaration of a national emergency at the southern border, appearing to provide the crucial vote needed for the Senate to pass the measure.

“I stand with the president often, and I do so with a loud voice,” Mr. Paul wrote in an opinion piece published late Sunday on Fox News’s website. “Today, I think he’s wrong, not on policy, but in seeking to expand the powers of the presidency beyond their constitutional limits.”

“I cannot support the use of emergency powers to get more funding” for a wall along the border with Mexico, he wrote, “so I will be voting to disapprove of his declaration when it comes before the Senate.”

Mr. Paul joins three other Republican senators — Susan Collins of Maine, Thom Tillis of North Carolina and Lisa Murkowski of Alaska — in backing the resolution. His support appears to provide the slim majority Democrats need to send the measure to the president’s desk, offering a stinging repudiation of the declaration.