Hamilton, who withdrew from his media commitments on Wednesday following the death of Mercedes' non-executive chairman Niki Lauda, ended the running eighth hundredths of a second clear of team-mate Valtteri Bottas.
Sebastian Vettel, sporting a Lauda-inspired crash helmet in tribute to the former Ferrari driver, finished third, over seven tenths down on Hamilton.
— Formula 1 (@F1) May 23, 2019
Vettel, though, endured one nervy moment when he ran straight on at the first corner, Ste Devote, but narrowly avoided contact with the barriers before returning to the track.
Mercedes are racing for the first time since Lauda died on Monday. Their cars are adorned with the motif, "Danke, Niki", while team members are wearing black armbands. The Austrian's former teams, McLaren and Ferrari, are also running tributes on their cars this weekend.
The Silver Arrows, who head into Sunday's race after starting the season with an unprecedented five one-two finishes, have struggled on the streets of Monte Carlo in recent seasons as the slow-speed track has not suited their cars.
But their eye-watering advantage over the rest of the field on Thursday suggests they will again be the team to beat.
Verstappen's former team-mate Daniel Ricciardo, now with Renault, topped every practice session in Monaco last year before putting his Red Bull on pole and then holding off Vettel in the race to take the chequered flag.
Although Verstappen impressed in the opening session, splitting the Mercedes cars, he finished the day's final running sixth, nearly a full second down on Hamilton's best effort.
That was primarily due to his lack of running after his car sustained a water leak, with the Dutchman completing only 17 laps, in comparison to the 41 posted by Hamilton.
Elsewhere, Verstappen's team-mate Pierre Gasly finished fourth ahead of the London-born Thai Alexander Albon in an impressive fifth position for Toro Rosso.
In his home race, Ferrari driver Charles Leclerc ended the day only 10th. British novices' Lando Norris and George Russell finished 12th and 19th on the completion of their first Formula One day in Monaco.