Coalition members filed a federal lawsuit in Los Angeles in September against the United States Citizenship and Immigration Services, the agency that reviews the applications, challenging the processing delays.

The federal agency has blamed the delays on a sharp rise in applications.

“U.S.C.I.S. continues to adjudicate the pending naturalization caseload, which skyrocketed under the Obama administration, more than doubling from 291,800 in September 2010 to nearly 700,000 by the beginning of 2017. Now, despite a record and unprecedented application surge workload, U.S.C.I.S. is completing more citizenship applications, more efficiently and effectively — outperforming itself,” Michael Bars, an agency spokesman, said in response to emailed questions.

There have been bigger application spikes in the past, such as in 2007, when the caseload swelled to 1.4 million and the agency was able to work through the backlog by the following year. That has not happened with the current pileup.

A total of 750,793 applications were pending at the end of June, the latest period available. But the rate at which they are being processed is at the lowest in a decade, according to an analysis released this month by Boundless Immigration, a technology company in Seattle that helps immigrants obtain green cards and citizenship. The agency was able to work through only about half its applications in 2017, compared to about 60 percent in 2016. (Data for 2018 is not available.)

“Applications for citizenship have surged many times in the past and U.S.C.I.S. was able to bring enough resources to bear to tame them. Wait times have doubled and the agency is barely processing half of their backlog,” said Doug Rand, a founder of Boundless Immigration.

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A Feb. 12 letter to the director of Citizenship and Immigration Services that was signed by 86 members of Congress raised concerns about the “alarming growth in processing delays” for naturalization and other services like green cards and visas.

It noted that the agency’s proposed budget for the 2019 fiscal year included a request that more than $200 million of its fee revenue be transferred to Immigration and Customs Enforcement, the agency that rounds up people for deportation.