Obama still leads 47 to 45 percent, but that’s down from 48 to 43 in the same poll from July, and 51 to 41 in the same poll from May.
Neither candidate is very popular in Iowa, with Obama registering a negative job approval rating and Romney a negative favorability rating.
Obama’s narrow lead is likely due to unaffiliated voters, who prefer the president 49 to 36 over Romney.
Obama campaigned at Iowa State University on Tuesday while Republicans held their convention in Florida.
Obama has now campaigned in Iowa for four days in August.
Two weeks ago the 2012 presidential campaign’s focus fell on Iowa as Obama and Republican vice presidential candidate Paul Ryan waged an intense battle for the state’s six electoral votes.
The competing visits to the relatively small state shows how important every electoral vote is for both campaigns in an election likely to be decided by a handful of battleground states.
Iowa is one of 12 key swing states the president won in 2008 that the GOP is looking to reclaim. Obama defeated Sen. John McCain (R-Ariz.) in the Hawkeye State by 10 percentage points in 2008. With the exception of 2004, Iowa has gone to the Democratic candidate in every election since 1988.