That was up from 2,229 reported in the state the week before.
Over the first three days of this week, initial claims continued to track at record levels, the agency said.
Almost every state cited COVID-19 for the jump in initial jobless claims, with heavy impacts in food services, accommodation, entertainment and recreation, healthcare and transportation, the report said.
Jobless claims in NY rose an unprecedented 520% last week, the first week in which claims were impacted by the coronavirus pandemic.
Revenue has collapsed at restaurants, hotels, movie theaters, gyms and airlines. Others came from health care and retail.
Almost 3.3 million people registered to claim unemployment benefits for the week ended 21 March, according to Department of Labor data. In the same week of 2019, only 215,000 new claims were registered. The agency has also doubled the number of workers processing unemployment claims.
"This data shows the enormity of the situation unfolding in our state", says Suzi LeVine, Employment Security Department Commissioner, in a news release. The week prior, 4,016 had filed jobless claims, marking an increase of 36,492 claims in a single week.
The New Mexico Department of Workforce Solutions is encouraging New Mexico residents who are filing for unemployment to do so online, which should make it easier for the state to respond quickly.
"The scale of increased demand for the unemployment system as a result of COVID-19 is unprecedented".
Last week 3,667 Vermonters lost their jobs and applied for unemployment insurance.