The DOL reported:

In the week ending April 3, the advance figure for seasonally adjusted initial claims was 744,000, an increase of 16,000 from the previous week’s revised level. The previous week’s level was revised up by 9,000 from 719,000 to 728,000. The 4-week moving average was 723,750, an increase of 2,500 from the previous week’s revised average. The previous week’s average was revised up by 2,250 from 719,000 to 721,250.
emphasis added

This does not include the 151,752 initial claims for Pandemic Unemployment Assistance (PUA) that was down from 237,065 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 increased to 723,750.

The previous week was revised up.

Regular state continued claims decreased to 4,067,784 (SA) from 4,200,238 (SA) the previous week.

Note: There are an additional 7,553,628 receiving Pandemic Unemployment Assistance (PUA) that increased from 7,350,339 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 5,633,595 receiving Pandemic Emergency Unemployment Compensation (PEUC) up from 5,516,487.

Weekly claims were higher than the consensus forecast.