Jason Bourne, which sees Matt Damon return to the lead role, is the fifth instalment of the franchise.
Last week's number one - Star Trek Beyond - dropped a place after taking a further $24m (£18.1m) over the weekend.
Bad Moms, a comedy starring Mila Kunis and Kristen Bell, took $23.4m (£17.7m) to debut at number three.
The Secret Life of Pets dropped to number four with takings of $18.2m (£13.8m).
Horror film Lights Out rounded off the top five with $10.8m (£8.1m).
Elsewhere in this week's top 10, thriller Nerve - starring Emma Roberts and Dave Franco - landed in eighth place with takings of $9m (£6.8m) on its first weekend of release.
Jason Bourne marks Damon's first appearance as the character since 2007 - when he starred in The Bourne Ultimatum, the third film in the series.
Jeremy Renner starred in the fourth, The Bourne Legacy, which was released in 2012.
Damon is also set to appear in forthcoming movie The Great Wall - reportedly the most expensive Chinese film in history.
But his casting has caused controversy, with some fans questioning why an Asian actor was not chosen for his role.
Follow us on Twitter @BBCNewsEnts, on Instagram, or email entertainment.news@bbc.co.uk.
The latest film in the Bourne series has topped the US box office after taking $60m (£45.3m) on its opening weekend.