Also starring Judi Dench, Ben Whishaw, Ralph Fiennes and Naomie Harris, the new film has set a new Bond box office record, as earlier predicted by analysts.
The record is for the biggest opening for a Bond movie in the US, not accounting for inflation.
Skyfall is now likely to be the highest-grossing Bond movie of all time, ahead of 2006's Casino Royale, which took $594m (£373m) globally.
Skyfall knocked out the animated Disney picture Wreck-It-Ralph from the number one spot, pushing it to second place with $33m (£20.7m).
Ben Affleck's Argo slipped to fourth place, earning $6.7m and bringing its total gross to $44.5m, while Taken 2 remained in fifth place from last week, earning $4m (£2.5m).
Rounding out the top ten are Here Comes the Boom, Cloud Atlas, Pitch Perfect, The Man with the Iron Fists and Hotel Transylvania.
The top ten in full (studio estimates):
1. (-) Skyfall - $87.8 million
2. (1) Wreck-It Ralph - $33 million
3. (2) Flight - $15.1 million
4. (3) Argo - $6.7 million
5. (5) Taken 2 - $4 million
6. (9) Here Comes the Boom - $2.55 million
7. (6) Cloud Atlas - $2.52 million
8. (11) Pitch Perfect - $2.50 million
9. (4) The Man with the Iron Fists - $2.49 million
10. (7) Hotel Transylvania - $2.35 million
Watch an exclusive Skyfall featurette below: