They believe modifications to their car will improve its pace at the street track after McLaren struggled at similar circuits earlier in the year.
Hamilton said: "We head into the weekend with renewed confidence following some positive tests and some developments in the wind tunnel."
Button added that "a lot had changed" since McLaren's poor race in Hungary.
The Hungaroring, like Singapore, is a low-speed track requiring high-downforce and McLaren were nearly two seconds off the pace set by Red Bull at that race in July, and 0.5secs slower than Ferrari.
But following a controversy over flexible bodywork, teams have been forced to make modifications to their cars and McLaren believe this will hit Red Bull and, to a lesser extent, Ferrari.
In addition, McLaren are introducing some major aerodynamic developments to their car that they hope will make it more competitive.
Team principal Martin Whitmarsh said he was "feeling positive that we'll once again be in a position to race at the front".
Hamilton, who crashed out of the Italian Grand Prix on Sunday, heads into the Singapore race on 26 September five points adrift of Red Bull's championship leader Mark Webber.
Ferrari's Fernando Alonso is third, followed by Button and Red Bull's Sebastian Vettel. All five are covered by just 24 points - less than a driver earns for a win.
Button said: "The Singapore Grand Prix will be a very interesting weekend because I think it'll give us a clearer idea of the destiny of the world championship.
"The last time we were at a low-speed, high-downforce track was in Hungary back at the start of August.
"Our car wasn't particularly competitive there, and maybe we haven't had a properly representative view of the top teams' relative pace because we've just visited two high-speed circuits.
"But, equally, a lot has changed since that race in Budapest - not least, some quite hefty revisions to the rulebook regarding bodywork flexibility and, additionally, a lot of work by the engineers at McLaren to ensure our car is now better suited to slower circuits.
"Singapore will be interesting for all of us - we'll not only get an idea of the speed of the Ferrari and Red Bull, but we'll get to see for the first time whether all our efforts over the past two months have helped put us back in the ballpark at high-downforce tracks."
Hamilton, who won in Singapore last year, added: "It's difficult to say accurately how competitive we'll be in Singapore.
"If Monza most closely resembled a track like Canada, then Singapore is far closer to places like Monaco and Hungary, where we've struggled relative to the competition.
"But the engineers are positive that we've made some good progress, so I'm looking forward to getting out on track and sampling the changes for real.
"The race should give us a clearer indication of exactly where we stand as the championship closes down over the next five races, but I definitely want to score as many points as possible in this grand prix."
Andrew Benson blog - BBC
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