Mercedes had topped the weekend's opening session through 2016 race victor Lewis Hamilton, but slipped down the order in FP2, with Bottas 10th and Hamilton eighth.
A second qualifying was scheduled for later on Thursday, final practice and qualifying on Saturday, then Sunday's 78-lap race.
'We didn't have the greatest day today, ' said Hamilton.
"That side will be a part of it for both of us, seeing as it's such a long year", Hamilton said.
Even the normally inscrutable Raikkonen sounded upbeat.
After finishing well off the pace in the afternoon, MercedesdriverValtteri Bottas said: "Practice two was hard and we struggled with the pace over one lap".
By contrast, the mood inside the Mercedes camp was likely to be one of concern.
"We were good in P1 (first practice) but something went wrong in this session".
"It was getting better and better", said the Finn.
Buoyed by his win at the last round in Spain, having come back after an indifferent weekend in Russian Federation when he could not find the right set-up for his vehicle, Hamilton had been optimistic that Mercedes had moved further forward and were well-prepared for Monaco.
"Ferrari generally are able to switch their tyres on a little bit easier than us, does that mean that we are in trouble this weekend or not?"
It was the first time Button has driven a 2017 spec vehicle and he admitted the new machines will take some getting used to.
"We put some good laps together and know where we need to improve so I'm very happy with our position after the first day". "But pretty sure there was a reason, they will be back to full force on Saturday".
Monaco is unique in F1 schedule, especially because the drivers get off on Friday. "It gives the guys here more time to work on the vehicle, spread over two days, rather than everything tonight". "We're looking forward to a real fight on Saturday".
The second session was briefly red flagged with half an hour remaining when Canadian rookie Lance Stroll, testing the limits on his first Monaco weekend, hit the barriers hard at the entrance to Casino Square. The 18-year-old Canadian crashed into the barriers near Casino Square, bringing the session to a brief halt while his vehicle was lifted off the track.
Max Verstappen was sixth fastest ahead of Sergio Perez while Mercedes failed to show its true speed in FP2 as Hamilton and Valtteri Bottas were over a second off the pace in eighth and tenth.
But while it was Hamilton who topped the order, all eyes were on his former team-mate Button, with the 2009 world champion returning to the McLaren cockpit just five races after he left the sport.
Williams, meanwhile, led the tributes to the victims of the Manchester terror attack after they ran #Manchester on the front of their cars.
The Mercedes team expressed concern before the weekend that their auto would struggle for agility around the demanding and technical corners.
78 - Monaco is the shortest circuit now being used (3,337 kilometres), subsequently it is also the race with the most laps (78).
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