The number of people applying for jobless benefits fell last week, and an independent firm estimated that private employers added 201,000 jobs in August, raising hopes that the rocky job market is improving ahead of the government’s monthly unemployment report on Friday.

Economists polled by Bloomberg estimate that employers added 125,000 jobs in August and that the nation’s unemployment rate remained unchanged at 8.3 percent.

Friday’s Labor Department report is more eagerly anticipated than most. It is one of only three jobs reports remaining before the Nov. 6 presidential election. And it will come just hours after President Obama claims his party’s nomination at the Democratic National Convention, capping a meeting where Democrats have argued before the nation that the economy , while struggling, is on the right track.

Republican presidential nominee Mitt Romney has accused Obama of mishandling the economy, and the report’s headline numbers may go a long way toward shaping voters’ views about who is right.

The report also comes just days before next week’s meeting of Federal Reserve policy makers. Federal Reserve Chairman Ben S. Bernanke said last week that economic growth is far from satisfactory and vowed that unless things improve, the Fed would be “forceful” in taking action to stimulate more robust growth. A weak jobs number could provoke the Fed to further push down already low interest rates to pump up the economy.

In July, employers added 163,000 jobs, a welcome change from three consecutive months in which the nation added an average of just 73,000 jobs. That figure is far lower than what is needed to keep up with normal workforce growth and to lower the nation’s unemployment rate. Overall this year, the economy has added an average of 151,000 jobs a month.

A recent flurry of economic indicators points to a gradual improvement in the job market, many economists say.

An employment report from payroll services firm ADP showed an increase of 201,000 private-sector payroll jobs in August. Thursday’s report from ADP was the strongest in five months.

The Institute for Supply Management’s non-manufacturing employment index increased in August, even though the group’s manufacturing index declined for the third consecutive month.

Meanwhile, the Labor Department reported Thursday that weekly unemployment claims were at 365,000, down from 377,000 the previous week.

Although economists predict some improvement, they do not expect a marked change in a job market where the unemployment rate has been above 8 percent for 42 consecutive months and the average length of joblessness for those who remain in the labor force is nearly 39 weeks. The National Employment Law Project, a worker advocacy group, issued a report saying that 6 million workers have exhausted their unemployment benefits since the economic downturn took hold in 2007.

With the expiration in the coming months of federal laws extending emergency jobless benefits, two million more unemployed workers could lose their benefits by the end of the year, the group said.

“Unemployment insurance has been a vital lifeline for millions of unemployed workers, helping them meet their families¨basic needs while they search for work,¨said Christine Owens, executive director of NELP. “. . .thanks to the prolonged jobs crisis and recent cuts to unemployment insurance programs, millions are left without any jobless aid.”