Of the 1,012 people surveyed from any party, only 30 percent said the process was working the way it should, down from 37 percent who said the same thing in January.
The difference was more stark for GOP voters. Gallup found 30 percent of Republicans and Republican-leaning independents thought the process was working, down from 46 percent who believed in the system in January.
The views of Democrats and Democratic-leaning independents were only slightly higher, at 32 percent approval, and had not changed significantly in recent months, according to Gallup.
The numbers came from telephone interviews conducted March 16-17 with a random sample of adults living across the nation.
It was not entirely clear what caused the shift in views on the election process. Gallup speculated the shift was likely due to GOP front-runner Donald Trump's polarizing campaign or the establishment GOP's efforts to stop him.
As evidence for the possible cause, Gallup pointed to the 68 percent of voters who believed at least one candidate for their party's presidential nomination would make a good president. The company also pointed to a recent New York Times/CBS News survey which found that 60 percent of Republican voters felt the party's presidential campaign made them feel "mostly embarrassed by the Republican Party rather than mostly proud."
"Republican establishment leaders' attempt to prevent Trump from getting the GOP nomination may be adding to rank-and-file Republicans' views that the process is not working, either because they support or because they oppose these efforts," Gallup said in an analysis of its survey results.
According to the company, which conducted similar polls during the 2000, 2008 and 2012 election cycles, Americans were most optimistic about the process when polled in January 2008. As Barack Obama, Hillary Clinton, John McCain and Rudy Giuliani battled for their party's nomination, 67 percent said they believed in the process.
Just three years later, faith in the election process plummeted to what was then its lowest point. As Barack Obama campaigned for re-election and Republicans worked to find their nominee, only 39 percent of Americans said the process was working as it should.