Double world champion Verstappen's best effort of one minute 12.462 seconds was just 0.065 quicker than Leclerc's fastest around the treacherous city streets and came after the Dutch driver had struggled with the car's set-up.
Leclerc will be going for his third successive Monaco pole position on Saturday and hoping for a first home podium on Sunday.
Ferrari's Sainz, who was quickest in the opening session with a lap of 1:13.372, was third fastest in the second but crashed after clipping the barriers at the exit to the Swimming Pool chicane.
The impact broke the car's front right suspension, with red flags waved to halt proceedings.
"Yeah, I crashed. Sorry," the Spaniard told the team, who had company president John Elkann keeping a close eye on proceedings, over the radio.
Compatriot Fernando Alonso was fourth fastest for Aston Martin ahead of a race he has won twice before and believes he can win again.
Alonso, four times third-placed on the podium from five races so far this season, had been second in the day's opening session that was twice red-flagged after drivers hit the barriers.
Seven-times world champion Lewis Hamilton steered his new-look Mercedes, with significant changes to side pods and suspension, to the third-best time in practice one and sixth in the second.
Last year's winner Sergio Perez, now 14 points behind Verstappen in the championship, was fourth and seventh respectively for Red Bull.
Perez had warned before the start of the track action that Monaco was not Red Bull's strongest circuit, despite the champions going unbeaten so far in 2023 with four one-two finishes and winning the last two editions of the race.
The Mexican identified the Ferrari drivers and Alonso as the biggest threats, a prediction that looked on the money for Friday at least.
The first session ended three minutes early when the red flags came out after Alex Albon crashed his Williams at the exit to the Sainte Devote first corner, wrecking the left side of his car.
Albon returned for the second session with a replaced gearbox and changes to the rear and front wings, suspension and floor.
Practice was also suspended when Nico Hulkenberg clipped the barrier and spun his Haas at the Nouvelle Chicane after the tunnel.
McLaren's Lando Norris was seventh and fifth fastest.
The Mercedes was the centre of attention when all the cars were displayed in the pitlane before the session and trackside engineering director Andrew Shovlin reserved judgement.
"We haven’t seen major problems which is a useful start to it. We were doing some comparisons on set-up across the cars so I think we have a good direction there - Lewis appeared to be in a happier place than George (Russell)," he said.
"It’s a good start but we’re certainly wary of the many ways you can get Monaco wrong.
"Monaco is about confidence for the driver. Lewis had that this morning but George didn’t so it’s about working on the tweaks that will bring that."
Russell was 15th and 12th fastest in the respective sessions.
