Hamilton, who left McLaren for Mercedes this season, used a brief dry spell in the morning to record a time of 1 minute, 23.282 seconds on the fourth and final day of preseason testing at the Catalunya Circuit.
"I think people are talking us up at the moment," said Hamilton. "(Sebastian) Vettel, and maybe Fernando (Alonso), were saying I'm maybe going to be competing for the world championship, but I really don't see that happening at the moment.
"Of course that's our goal, but you have to remember the car was over a second off (the pace), sometimes two seconds off, last year and we've not caught up a second. Hopefully by the end of the year. That's our goal, but definitely not at the beginning."
Practice was interrupted by eight red-flag stoppages due to the slippery conditions, which gave several drivers problems staying on the track.
While the rain and delays from spin-offs didn't allow teams to get in many laps or long runs, it did offer the opportunity to try out Pirelli's new wet and intermediate tires.
Hamilton's former teammate Jenson Button steered his McLaren to the session's second-best lap, while Jean-Eric Vergne of Toro Rosso was next.
Hamilton had gotten off to a rough start with his new team in testing at the Jerez track earlier this month when a brake failure sent him straight into the barrier. Now it appears that both he and Nico Rosberg are adjusting well to the car. Rosberg clocked the fastest lap time during Tuesday's session.
"Nico and Lewis are becoming more familiar with the car and its behavior as each day progresses, and Lewis is settling into the team very well," Mercedes team principal Ross Brawn said. "We now have just four days of testing left until the first race in Australia, and a lot of work will be done before we return to Barcelona next week."
Preseason testing returns to northeastern Spain from Feb. 28-March 3 before the season-opening Australian Grand Prix on March 17.
Jules Bianchi, who is competing with Adrian Sutil to be named a Force India pilot along with Paul di Resta, helped his cause by putting in the fourth quickest effort on the day.
Bianchi was also the busiest driver with 96 laps completed. Vergne and Ferrari's Felipe Massa came next with 80 laps each as all drivers were hampered by the damp surface and constant stops and starts.
Massa was the rain's first victim just 10 minutes into the session when he went off the track and nudged his car into the barrier.
Giedo van der Garde of Caterham caused two red flags, while Vergne, Sauber's Esteban Gutierrez, Mark Webber of Red Bull, Hamilton and Bianchi all needed assistance at one point during the day.
Pastor Maldonado and rookie Valtteri Bottas again took turns behind the new Williams car, with neither recording a flying lap time.