According to the Realmeter survey, support for Moon gained 2.1 percentage points over the week to 63.2 percent last week. It was the first increase in seven weeks.
The result was based on a poll of 2,505 voters conducted from last Monday to Friday. It had 2.0 percentage points in margin of error with a 95 percent confidence level.
Moon's order to disband and create a new military intelligence unit gained public support as the Defense Security Command (DSC) was charged with preparing to invoke martial law to crack down on candlelit rallies that led to the impeachment of former President Park Geun-hye.
The Moon government unveiled emergency measures last week to help people suffering from scorching heat wave, while taking actions to tackle negative effects from the surge in minimum wage. Those measures helped Moon win support from voters, the pollster said.
Moon's ruling Democratic Party kept its top post with 42.8 percent in approval rating that was down 1.2 percentage points from the previous week.
Support for the main conservative opposition Liberty Korea Party fell 1 percentage point to 17.6 percent last week.
The minor progressive Justice Party kept a record-breaking trend, garnering 14.3 percent in support scores.
The minor conservative Bareun Future Party won 5.8 percent of support, and the centrist Party for Democracy and Peace gained 2.8 percent last week.