Donald J. Trump’s presidency has been so full of departures from the norms of international relations that uncertainty has seeped into the calculation of America’s plans. That has subjected the dollar to additional skepticism, enhancing the fundamental factors pulling it down, from worries about the strength of the American economy to improved fortunes in Europe and Asia.

The dollar has in some sense become an international medium of expression about the American political environment. Its value offers a gauge of sentiment for Mr. Trump’s prospects in achieving his economic goals, as well as worries about his potentially impulsive declarations.

“At the margin, investors may be a little more cautious in treating the dollar as safe haven,” said Jeremy Cook, chief economist at World First, a London-based company that handles foreign exchange transactions. “Certainly, the sentiment toward the viability of the Trump administration has not helped. There’s the risk that at 3 a.m., Trump tweets something and the dollar gets hit.”

Before Mr. Trump was even sworn in, many investors were buying into the so-called Trump trade, a bet that the new president’s plans for tax cuts, deregulation and a hefty dose of infrastructure spending would spur economic growth. This formulation has earned favor in the stock market. During the Trump administration, American shares have reached new highs, propelled by strong corporate profits and executives exuding optimism.

Yet the Trump trade was also a wager that the dollar would climb as investment flooded into the United States to exploit fresh growth opportunities.