“This report shows, once again, that our current immigration system jeopardizes our national security,” said a White House fact sheet promoting the findings, which were compiled by the Departments of Justice and Homeland Security.

Over recent days, the debate over a potential immigration compromise has devolved into a bickering match over racially charged comments and profanity-laced phrases. Tuesday’s report was an attempt by the Trump administration to use government-compiled data to make a loftier, policy-based argument about the president’s push for a merit-based immigration system.

Testifying on Capitol Hill, Kirstjen Nielsen, the homeland security secretary, called the report’s findings “truly chilling data.” She pointed to the case of Abdurasul Hasanovich Juraboev, an Uzbek man who was admitted to the United States in 2011 through the diversity visa lottery, a State Department program that allows in immigrants from countries that do not send many people to the United States. He pleaded guilty in 2015 to conspiring to support the Islamic State after posting a threat on an Uzbek-language website to kill President Barack Obama in an act of martyrdom.

Mr. Trump is seeking to end the visa lottery and enact new restrictions on immigrants’ ability to bring members of their extended families to the United States as part of an immigration compromise currently under discussion.

But the statistics were notable as much for what they did not contain as for what they did.

They included cases — a senior administration official who insisted on anonymity to detail the report could not say how many — in which foreigners were extradited to the United States to face trial. That means they did not, in fact, enter the country “through our immigration system,” as the White House fact sheet asserted.