Experts warn that the administration’s haphazard use of tools that freeze assets and cut people and countries off from the world’s banking system could undermine the entire program by spawning new workarounds.

“Sanctions alone will never solve your problem unless they are used in tandem with other tools,” said Matthew Levitt, a fellow at the Washington Institute for Near East Policy. “We tend now to be seeing sanctions as the nonkinetic, nonmilitary tool for everything.”

Mr. Levitt, who served as deputy assistant secretary for intelligence and analysis at the Treasury Department during the George W. Bush administration, added, “I do worry about a time when overreliance on sanctions, absent the use of complementary diplomatic and other tools, could undermine the U.S. position in the world economy.”

There have been early signs of such a shift.

Over the past year, the European Union has rolled out the Instrument in Support of Trade Exchanges, or INSTEX, as an alternative to the Swift financial messaging service, which facilitates the majority of international financial transactions. It would allow European countries to complete transactions with Iran through what is essentially a bartering system. While Europe has said that it would use this only for sales of humanitarian goods, which are acceptable, the United States has expressed concern that the payments vehicle could be used to evade sanctions.

Venezuela and North Korea have also increased their interest in cryptocurrencies, which could be used to circumvent the traditional banking system, according Peter Harrell, a sanctions expert at the Center for a New American Security. And Russia has shifted billions of dollars’ worth of sovereign reserves, which are held in American banks, into gold as a way to reduce the potential effect of additional sanctions.

Sign up for On Politics to get the latest election and politics news and insights. Sign up for our politics newsletter

“The question is are we now reaching the point where both adversaries and allies will invest in the kinds of tools that will let them fundamentally get out from under our leverage,” Mr. Harrell said. “We are seeing signs that they are pursuing these investments.”

The future of such investments could hinge on Mr. Trump’s re-election. John E. Smith, who was the director of the Treasury Department’s Office of Foreign Assets Control until last year, said that other countries would most likely move to further distance themselves from America’s teeth if Mr. Trump wins a second term.