The plunge in New York City’s unemployment rate continued in October, falling to 6.4 percent, its lowest level in six years, the state’s Labor Department reported on Thursday.

The rate, which dropped from 6.8 percent in September, brought the decline in the city’s unemployment over the past three months to 1.4 percentage points, the steepest decline in any quarter in the 38 years on record, the department said. The decrease brings the unemployment rate more in line with the reports on job creation, which are generated by a separate monthly survey.

Throughout the recovery from the last recession, the estimated number of private-sector jobs has been rising as fast or faster for the city than for the country as a whole. But the unemployment rates, which are derived from surveys of households, have told a very different story, indicating that hiring was lagging in the city.

As recently as July, the Labor Department was reporting that the city’s unemployment rate was 1.8 percentage points higher than the nation’s. Now, that gap is closing; the national unemployment rate for October was 5.8 percent.