The DOL reported:

In the week ending March 13, the advance figure for seasonally adjusted initial claims was 770,000, an increase of 45,000 from the previous week’s revised level. The previous week’s level was revised up by 13,000 from 712,000 to 725,000. The 4-week moving average was 746,250, a decrease of 16,000 from the previous week’s revised average. The previous week’s average was revised up by 3,250 from 759,000 to 762,250.
emphasis added

This does not include the 282,394 initial claims for Pandemic Unemployment Assistance (PUA) that was down from 478,914 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 759,000.

The previous week was revised up.

Regular state continued claims decreased to 4,124,000​ (SA) from 4,142,000 (SA) the previous week and will likely stay at a high level until the crisis abates.

Note: There are an additional 7,615,386 receiving Pandemic Unemployment Assistance (PUA) that decreased from 8,387,969 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 4,815,348 receiving Pandemic Emergency Unemployment Compensation (PEUC) down from 5,456,080.

Weekly claims were higher than the consensus forecast.