The DOL reported:

In the week ending March 27, the advance figure for seasonally adjusted initial claims was 719,000, an increase of 61,000 from the previous week’s revised level. The previous week’s level was revised down by 26,000 from 684,000 to 658,000. The 4-week moving average was 719,000, a decrease of 10,500 from the previous week’s revised average. This is the lowest level for this average since March 14, 2020 when it was 225,500. The previous week’s average was revised down by 6,500 from 736,000 to 729,500.
emphasis added

This does not include the 237,025 initial claims for Pandemic Unemployment Assistance (PUA) that was down from 241,137 the previous week.

The following graph shows the 4-week moving average of weekly claims since 1971.

Click on graph for larger image.

The dashed line on the graph is the current 4-week average. The four-week average of weekly unemployment claims decreased to 719,000.

The previous week was revised down.

Regular state continued claims decreased to 3,794,000 (SA) from 3,840,000 (SA) the previous week.

Note: There are an additional 7,349,663 receiving Pandemic Unemployment Assistance (PUA) that increased from 7,844,867 the previous week (there are questions about these numbers). This is a special program for business owners, self-employed, independent contractors or gig workers not receiving other unemployment insurance.  And an additional 5,515,355 receiving Pandemic Emergency Unemployment Compensation (PEUC) down from 6,220,492.

Weekly claims were higher than the consensus forecast.