Max Verstappen headed team-mate Daniel Ricciardo in the first session and stayed on top in FP2 with Ricciardo third. He finished the second session in 10th. "This circuit is a tough one", Hamilton said.
This weekend marks the eighth round of the 2017 Formula One championship, with the series returning to Azerbaijan and the Baku street circuit for the second time. "Now it's just a case of getting our heads together tonight to work out exactly how to extract that pace across the entire weekend".
The super-soft runs were interrupted at the halfway point when the narrow, twisty Turn 8 claimed its second F1 auto of the day, as the Renault of Jolyon Palmer ground to a halt in the barriers with broken right-front suspension.
Hamilton, a victor last time out in Canada, failed to set a time on the super-soft tyre, the quickest of the three Pirelli compounds available here, after falling foul to Sergio Perez's crash and then traffic.
Verstappen, meanwhile, was down to a 1:44.288 and then a 1:43.988 and a 1:43.894.
McLaren is the only team yet to score a point, and continues to be blighted by its unreliable Honda engine, prompting growing speculation that management is out of patience and considering a deal with Mercedes as its engine supplier.
"Ferrari and Mercedes can improve, we have to be careful, but we are closer", Verstappen said.
Red Bull's Ricciardo ended his day in third place and was satisfied with the improvements that the team made across the day.
When it got underway, track temperatures were at a blistering 54 degrees C (129 degrees F).
His subsequent lap time gains put him in the 1m43s margin and he ended his first run with a best lap of 1m43.894s.
It promises to be a tricky one.
The Force India driver was one of the more impressive drivers in Baku previous year, and had been flying through the city circuit before his collision late on.
Daniil Kvyat was the lead Toro Rosso in eighth, splitting the two Force Indias of Sergio Perez and Esteban Ocon, despite having triggered a brief virtual safety vehicle in the first half of the session, as he put debris on track from barrier contact at the sharp right-handed Turn 15.
Drivers were being severely tested in other sections, too.
Palmer's incident, midway through the 90-minute session, resulted in the action being temporarily suspended as they removed the under-fire Briton's mangled Renault and the ensuing debris. The two Saubers moved off the very bottom of the timesheets as Romain Grosjean struggled to 20th in the second Haas.