In the week that ended Saturday, initial claims rose to 374,000 from 308,000, a figure from the previous week that was left unrevised.
The jolting numbers were the result of continued computer problems in California and to furloughed workers at defense contractor companies and other businesses that rely on a functioning government to stay busy.
The National Employment Law Project noted furloughed workers at government contract firms can apply for unemployment benefits and for the most part do not need to look for work while they are laid off, given the high expectation the layoff is temporary.
Among the firms where work has been derailed is Lockheed Martin that said it will furlough 2,400 workers, Lawrence Livermore, where 6,000 jobs are in jeopardy of furlough and SAIC in Tennessee that has furloughed 1,000 employees.
"These are only a few examples of what will be increasingly happening throughout the country as the shutdown continues," NELP said.
The four-week rolling average for first-time claims rose by 20,000 from the previous week, climbing from 305,000 to 325,000, the Labor Department said.
Claims rose unexpectedly. Economists had forecast a climb to 312,000.
The weekly report may be surprising just by itself. The federal government is largely not releasing economic reports during the shutdown, but the weekly unemployment benefit claims numbers, which come from the Labor Department, are compiled mostly by state governments.
The largest increases in initial claims for the week that ended Sept. 28 were in Puerto Rico where claims rose by 1,105, Oregon, up by 1,104 and California with 1,045 additional claims. The largest decreases were in Michigan, down by 2,061, New York, down by 1,694, and Florida with 1,349 fewer claims.
2014: The Year in Music [PHOTOS]