Rasmussen said its survey, released Monday, indicated 50 percent of likely voters said they trusted Obama more than Mitt Romney, while 40 percent said they trusted Romney more.
Voters were asked which presidential candidate they trusted more on immigration, the war in Afghanistan, Social Security, education, and government ethics and corruption.
The Rasmussen Reports daily Presidential Tracking Poll for Monday indicated Obama was supported by 50 percent of voters nationwide while Mitt Romney earns support from 45 percent. Two percent said they preferred another candidate and 3 percent said they were undecided.
Rasmussen said it was Obama's largest lead over Romney among likely voters since March 17.
Results of the trust survey are based on a nationwide survey of 1,000 likely voters conducted Friday and Saturday. The margin of error is 3 percentage points.
The Presidential Daily Tracking Poll results are based on data collected via telephone surveys of 500 likely voters a night and reported on a three-day rolling average basis. The margin of error in the sample of 1,500 likely voters is 3 percentage points.