The 37-year-old Briton is back in a grand prix car - just five races after he stepped down from the sport - as a replacement for Fernando Alonso, who is taking part in the Indianapolis 500.
Button eased his way back into action on Thursday before finishing 14th in the order during opening practice and then 12th following the conclusion of the day's second running.
The Englishman was just four hundredths of a second slower than his McLaren team-mate Stoffel Vandoorne, and the low-nature speed of the famous Monte Carlo street circuit is likely to be among the best chances of a good result for the British team this season.
McLaren are propping up the constructors' championship, and are the only team who failed to score a single point from the opening five rounds.
"I definitely stepped away at the right time and I haven't missed driving a Formula One car," Button said.
"But today I really enjoyed it, more than I have for a couple of years to be fair. And that's two things: because the cars are better to drive and I haven't driven one for seven months.
"I enjoyed it and I tapped the barrier a couple of times. It's good to know that I'm pretty much on line and pushing the limits but no damage so far, so that's good as well.
"I think you've always got to think points are possible if you can finish the race. I've driven this car for about 65 laps now so there's more to come."
Button also stood by his x-rated outburst in which he shouted over the team radio: "People still drive like s***. Some things do not change."
"I don't think I said anything wrong," added Button, who refused to reveal which driver he aimed his frustrations at. "They deserved it. You have got to look in your mirrors at Monaco and it is a shame.
"It is the most frustrating thing when you are in a racing car and people slow down in front of you. They know you are on quick lap.
"There is so much change in Formula One. That is great, but some things never change and that is the driver-team radio. It is just respect to other cars and other drivers."
