The DOL reported:

In the week ending March 6, the advance figure for seasonally adjusted initial claims was 712,000, a decrease of 42,000 from the previous week’s revised level. The previous week’s level was revised up by 9,000 from 745,000 to 754,000. The 4-week moving average was 759,000, a decrease of 34,000 from the previous week’s revised average. The previous week’s average was revised up by 2,250 from 790,750 to 793,000.
emphasis added

This does not include the 478,001 initial claims for Pandemic Unemployment Assistance (PUA) that was up from 436,138 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.

The second graph shows seasonally adjust continued claims since 1967 (lags initial by one week).

Regular state continued claims decreased to 4,144,000 (SA) from 4,337,000 (SA) the previous week and will likely stay at a high level until the crisis abates.

Note: There are an additional 8,387,194 receiving Pandemic Unemployment Assistance (PUA) that increased from 7,329,172 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 5,454,740 receiving Pandemic Emergency Unemployment Compensation (PEUC) up from 4,468,389.

Weekly claims were lower than the consensus forecast.