- Formula One confirm two more races for 2020 including historic trip to Ferrari track at Mugello
- Sergio Perez puts Racing Point top of the practice timesheets
Hamilton's Finnish team mate Valtteri Bottas, the championship leader after winning Sunday's Austrian season-opener at the same Red Bull Ring circuit, was second and a mere 0.043 slower.
"We learned a bit more about the car, we were of course not so happy last week," said Verstappen, a two times winner in Austria who became the first retirement of the season last weekend.
"I'm a lot more pleased. It's heading in the right direction."
Bottas said Mercedes appeared also to have made progress on the reliability issues that raised stress levels during last weekend's race.
Mexican Sergio Perez, who put Racing Point's 'Pink Mercedes' on top in the morning session at Spielberg, ended the day with the third best time.
It was another tough day for Ricciardo, who brought out red flags in the afternoon after locking up and hitting the tyre wall at speed backwards at turn nine with only 13 minutes gone.
The Australian seemed to limp after clambering out of the car. Renault said he had gone to the medical centre for a check-up and been declared fit.
Hamilton ended the second session sixth, behind Canadian Lance Stroll in fourth for Racing Point and Carlos Sainz fifth for McLaren.
"It felt relatively normal but it's quite far off," Hamilton said of his car's performance. "There's a lot of work that needs to go on in the background to try and figure out why.
"I was feeling good in practice one and the start of P2 felt pretty good but then it just started to drop off...hopefully tomorrow we'll be in a better position."
With heavy rain forecast on Saturday, there were fears the second session could dictate the grid positions for Sunday's race, although Formula One has held qualifying on a Sunday before.
"It could be that maybe the entire Saturday is not happening," said McLaren principal Andreas Seidl.
"It could also be that Sunday morning is really bad. So worst case, the result from free practice two is defining the grid."
The Racing Point, whose 'Pink Mercedes' nickname comes from its similarity to the 2019 Mercedes that took Hamilton to his sixth championship, lived up to its reputation.
Perez lapped with a best time of one minute 04.867 seconds on soft tyres in the morning, with Verstappen putting in a 1:03.660 in the second session.
Ferrari were off the pace in both sessions as they evaluated new parts, with Sebastian Vettel 10th and Charles Leclerc 12th in the morning. Leclerc was ninth after lunch, Vettel 16th -- slower than George Russell's Williams.
Canadian rookie Nicholas Latifi stopped his Williams with an engine problem halfway through the first session, with McLaren's Lando Norris collecting a three place grid drop for not respecting the yellow warning flags.
Sunday's race, named after the southern Austrian state where the circuit is located, will be the first time a track has hosted two grands prix in the same season.