Daniil Kvyat set the pace in a wet second free practice for the Japanese Grand Prix, as the rain restricted the running once again.
Although the rain had stopped for the start of the session, the track was always very wet, and no one managed to run on slicks.
Kvyat's teammate Daniel Ricciardo was fourth, with Singapore GP winner Sebastian Vettel completing the top five for Ferrari, albeit nearly two seconds off the pace.
As the lights turned green, there was no hurry from most teams to get any early running done, with the track still very wet, even though the rain had stopped earlier.
Kvyat, however, broke the silence three minutes in, the Russian venturing out on intermediate tyres and setting the first timed lap of the session, which was already faster than the best FP1 time set by Carlos Sainz.
Rosberg took to the top of the times after 15 minutes, lapping a full second quicker than Kvyat as the conditions improved as more cars jumped onto the track.
Hamilton made it a Mercedes 1-2 on the timesheets, the Briton lapping over half a second slower than his teammate just minutes later.
As the session reached the 30-minute mark, most drivers had set a laptime.
The McLarens and Valtteri Bottas had not appeared on the timesheets, however, Fernando Alonso spending some 45 minutes in the pits as his McLaren team was forced to revert to his Singapore GP engine following problems during opening practice.
Teammate Jenson Button, like Bottas, took things easy and did not seem in a hurry to post a time. The Finn did not take to the track at all.
Max Verstappen also faced a delay as his Toro Rosso mechanics worked on his car, the Dutchman not taking to the track during the first 30 minutes of running.
Some 35 minutes in, Kvyat set a new benchmark - 1:48.277 - still on intermediate tyres, just beating Rosberg's time.
But the rain began again with some 50 minutes to go, making the laptimes significantly slower and reducing the number of cars on track.
First Marcus Ericsson and later Alonso ventured out with full wets in the final 30 minutes, but the running was scarce, with heavy rain hitting the circuit.
There were several incidents during the session as the drivers tried to find the grip limits, but none of significance.
|1||Daniil Kvyat||Red Bull Racing||1:48.277||6|
|4||Daniel Ricciardo||Red Bull Racing||1:49.097||+0.820||10|
|7||Carlos Sainz Jr.||Toro Rosso||1:50.418||+2.141||6|
|8||Max Verstappen||Toro Rosso||1:50.542||+2.265||5|
|10||Pastor Maldonado||Team Lotus||1:51.557||+3.280||7|
|11||Nico Hulkenberg||Force India||1:51.674||+3.397||11|
|14||Sergio Perez||Force India||1:52.070||+3.793||8|
|15||Romain Grosjean||Team Lotus||1:52.534||+4.257||6|