MIAMI — Thousands of immigrants who joined the United States military with promises of a fast track to citizenship are stuck in limbo as new screening measures have taken far longer than expected, leaving some military members around the nation unable to become citizens or even go to basic training.

In the Army alone, about 4,300 people are awaiting the completion of their background checks, said Hank Minitrez, a spokesman for the Army. Until they are cleared, they cannot enter basic training or deploy overseas, leaving them stuck on bases if they are on active duty.

Immigrants must be in the United States legally in order to enlist. But the new vetting measures, begun in the waning months of the Obama administration, have taken so long that by November, the legal status of up to 1,500 people who enlisted in active duty or the Reserve had expired while they waited for clearance, the Army said.

They cannot legally drive or find work, a problem for reservists, who do not draw a full-time military paycheck. Although the Army is granting some extensions, they could eventually be subject to deportation, the Army said.