"Witness," in which Perry infused political themes into pop music, sold 162,000 albums, 51,000 songs and was streamed more than 19 million times in its opening week, totaling 180,000 album units, according to figures from Nielsen SoundScan.

The Billboard 200 album chart tallies units from album sales, song sales (10 songs equal one album) and streaming activity (1,500 streams equal one album).

Perry's promotional tour included numerous performances, interviews and a four-day livestream on YouTube before the album's release.

In one interview, Perry said she was ready to bury the hatchet on her long-running feud with Swift.

Swift has yet to respond, but she released her back catalog to streaming services on the same day as Perry's "Witness" release in what was widely seen as a bid to steal Perry's thunder.

On Monday, Swift's 2014 album "1989" climbed to No. 31 on the Billboard 200 chart on the strength of nearly 19 million streams, just under the streaming figures for Perry's "Witness."

Perry became the second solo female artist to top the Billboard chart this year, following on last week's No. 1 debut from Halsey.

Other new releases in the top 10 this week include hip hop singer SZA's "CTRL" at No. 3, country music group Lady Antebellum's "Heart Break" at No. 4 and punk rock band Rise Against at No. 9 with "Wolves."

On the Digital Songs chart, which measures online single sales, Puerto Rican singer Luis Fonsi's "Despacito" featuring Justin Bieber continued its reign at the top, adding 140,000 copies sold.