Norris and teammate Oscar Piastri, separated by three points at the top of the championship, resumed normal service after Alpine's Pierre Gasly was surprise pace-setter in the first session.
The Briton lapped the super-fast floodlit Corniche circuit with a best time of one minute 28.267 seconds, 0.163 quicker than Australian Piastri.
"I think at the minute we feel confident, but the others are not far behind," said Norris.
"I was probably hoping for a bigger gap than what we had today. We know we're fast, we know we have a great car, but certainly not as comfortable as what we would like."
Red Bull's four-time world champion Max Verstappen lapped third fastest, 0.280 off the pace, before teammate Tsunoda brought red flags out with nine minutes remaining.
The Japanese, drafted in from Racing Bulls in a straight swap with Liam Lawson, clipped the kerb at the final corner and put his car into the wall. He was able to step out and walk away.
"I just turned in too much and clipped the wall and inside wheel. I had damage after that and just had no control," said Tsunoda.
"It is frustrating because the pace was looking good, so it’s a shame, but also a positive, as I was getting the car in a good window."
When practice resumed, there was only enough time for practice starts.
"Compared to Bahrain, the grip levels and set-up of the car is completely different, so it is very difficult to compare to last week, but it is still clear that we want to be faster," said Verstappen.
The Dutch driver, winner in Japan, was only sixth fastest in Bahrain last weekend - a race won by Piastri from pole with fastest lap.
Mercedes' George Russell was seventh in the second session, and sixth in the first, on what he said had been a "slightly messy day."
"We didn't manage to get too many clean laps in, owing to both traffic and a few efforts where we didn't quite get the tyres in the right window," Russell said.
"It's not controversial to say that McLaren looked like they were clear in front, but I'm hopeful we can be in the fight for best of the rest once again as we head into the weekend."
Gasly led the first session in 1:29.239 seconds, 0.007 quicker than Norris.
Ferrari's Charles Leclerc was third in that opener with Piastri, winner in Bahrain last weekend and hoping to become the first Australian to lead the championship since Mark Webber in 2010, fourth.
That session, run in the late afternoon sunshine on the shores of the Red Sea, was largely unrepresentative of the conditions for Saturday's qualifying and Sunday's race, which is held at night.
The session still served as a useful measure of driver confidence on a daunting track that rewards the gradual building up of pace.