WASHINGTON — Hiring rose last month in 14 U.S. states in June, and the unemployment rate fell to record lows in two states, evidence that the job market is getting tighter across much of the country. The Labor Department said Friday that unemployment rates fell in 10 states and rose in only 2. Rates were stable in the other 38 states.

After five years of steady hiring, unemployment rates have fallen below 4 percent in 23 states. Unemployment that low suggests that those states are at “full employment,” when nearly everyone who wants a job has one and the unemployment rate reflects the normal churn of hiring and firing.

The rate has fallen below 3 percent in five states: Colorado, Hawaii, Nebraska, New Hampshire and North Dakota.

When unemployment falls that low, businesses may be forced to raise pay to compete for scarce workers. So far, wage gains nationwide remain at about 2.5 percent a year, below the 3.5 percent pace normally associated with a healthy economy. North Dakota’s unemployment rate fell to 2.3 percent, a record low for the state dating back to 1976 and tying for lowest in the nation with Colorado. Tennessee’s rate of 3.6 percent is also a record low for that state.