Button fastest in second session
The duo of British former world champions, who between them have won the Melbourne race for the last three years, had been expected to struggle after reliability problems dogged their pre-season testing and forced a rejig of their car this week.
Button clocked one minute 25.854 seconds for the fastest time of the day in the second of the two sessions, however, with Hamilton 0.132 seconds behind to push Ferrari and Red Bull off the top of the timesheets.
"There's still lots to play for this weekend," Button said. "We've got a much-improved car and a much better balance and we can really build on that I think which is positive.
"Whatever happens this weekend, we should be very happy with the step forward we've made."
Spain's Fernando Alonso, runner up in the title race last year, was third quickest for Ferrari in 1.26.001, edging world champion Sebastian Vettel into fourth with a best lap of 1.26.014 in his Red Bull.
"I think we got a good idea of where we are compared to our competitors," said 23-year-old German Vettel. "All in all, I think we can be pleased, it seems we're not too bad."
"We've got some work to do, there were some quick guys out there," said Webber, who topped the times in the first session. "McLaren look quick, but with Ferrari you can never tell, as they always run a bit more fuel on a Friday."
Alonso said he thought the day had only proved that there were several teams who could win Sunday's race, making Saturday's qualifying all the more important.
"Nothing new yet and what would you expect," the twice world champion said. "These two free practice sessions have not actually revealed the real relative strengths of the teams.
"This morning Red Bull went well and this afternoon it was McLaren's turn with us and Mercedes always in the mix..."
After a two-week delay caused by the postponement of the Bahrain round of the championship because of civil unrest in the Gulf kingdom, the 12 teams finally got the season underway in earnest under leaden skies at Albert Park.
Rain fell towards the end of the second session and more is forecast for Saturday, although race day is predicted to be dry.
Mexican Sergio Perez finished an impressive eighth over both sessions in his Sauber, the best of the four rookie drivers.
The biggest cheer of the day came when Vitantonio Liuzzi emerged from the HRT garage for the team's first appearance on the track some two minutes from the end of the second session.
The Italian, who is partnered by Indian team mate Narain Karthikeyan at the team, managed a single lap before limping back to the pits.
Indian reserve driver Karun Chandhok's first drive in the Team Lotus car lasted less than a minute of the first session before he spun on the track and crashed into a barrier, smashing the front wing off the T128.