Defending five-time world champion and championship leader Hamilton wound up fourth-fastest after a frustrating opening day that saw Ferrari pair Charles Leclerc and Sebastian Vettel top a session each, with the Briton's teammate Valtteri Botas in third.
"Ferrari looks quite quick -- they're nearly a second quicker than us just in a straight line down to Turn Five. That's quite impressive, but we'll keep just chipping away at it. We're clearly in the mix, which is good."
Leclerc bounced back in the second session to upstage German team-mate Vettel on a warm and humid afternoon at the majestic Spa-Francorchamps circuit in the Ardennes forests.
Leclerc led with a best lap of one minute and 44.123 seconds to outpace four-time world champion Vettel by over six-tenths of a second, as Ferrari continued in the afternoon where they had left off in the morning's action, when Vettel led the Monegasque.
Bottas, confirmed on Thursday to be staying with Mercedes next season, was over eighth-tenths of a second off the pace, slightly ahead of Hamilton who experienced problems in the morning with a new engine.
"We had a problem with the throttle and I lost power. I was idling with the rpm just trying to get it back," said Hamilton.
"I managed to fix it with a couple of switch changes. When we went back out, we had another problem and it was a bit of a mess.
"I had a few laps towards the end, but nothing spectacular. Then we made some changes, because the set-up was quite far off going into FP2.
"It was feeling a lot better, but there's still a lot of work to do."
- Ferrari 'very fast' -
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Mercedes hope they may find an advantage over Ferrari in the second sector, where there are more corners and fewer straights -- but will likely struggle in the high-speed sector one.
Verstappen said he could not envisage Red Bull overhauling Ferrari.
"I think Ferrari will be very fast. I think they will be very hard to beat. We'll try to be close to Mercedes. We'll see what happens."
Daniel Ricciardo of Renault and Red Bull new boy Alexander Albon were ninth and 10th.
Practice ended prematurely when Sergio Perez's Racing Point car stopped with a fire around the exhaust system. A Virtual Safety Car was deployed and then the action was red-flagged, and with only two minutes remaining the session was not re-started.
Perez's fire followed a curious report from Stroll that he could smell burning in his sister car as he came in for a late pit-stop -- a warning that all may not be well with the latest Mercedes power unit also being used by Hamilton and Vettel.
Ferrari were the only major team and engine supplier not to introduce a revised engine this weekend.
"We also have a new engine, but it's coming later," said Vettel.
"I don't know what Mercedes have in the luggage, but I suppose we will find out on Saturday -- so until then I'm taking nothing for granted."