From the outset, Gary D. Cohn was an unconventional choice to be President Trump’s top economic adviser.

A former Goldman Sachs president and proponent of free trade, Mr. Cohn had a pedigree and economic views that clashed with Mr. Trump’s populist rhetoric and protectionist policies. His methodical approach also contrasted with the president’s freewheeling style.

But Mr. Cohn, who said on Tuesday that he would resign as director of the National Economic Council, brought to the Trump administration something that the president himself lacked: the widespread respect of top corporate executives.

Now, those business leaders are lamenting the loss of one of their own from what is among the country’s most important economic positions.