WASHINGTON — The Obama administration declassified a handful of details Tuesday that credited its PRISM Internet spying program with intercepting a key email that unraveled a 2009 terrorist plot in New York.

The details, declassified by the director of national intelligence, were circulated on Capitol Hill as part of government efforts to tamp down criticism of two recently revealed National Security Agency surveillance programs.

Najibullah Zazi’s foiled plot to bomb the New York subways has become the centerpiece of that effort. It remains the most serious al-Qaida plot inside the United States since the 9/11 terror attacks.

In the rush to defend the surveillance programs, however, government officials have changed their stories and misstated key facts of the Zazi plot. And they’ve left out one important detail: The email that disrupted the plan could easily have been intercepted without PRISM.

The debate over the surveillance echoes one from years earlier, over President George W. Bush’s warrantless wiretapping and harsh interrogation tactics. Critics said the government had gone too far but the administration said the techniques were lawful and kept America safe.

“What is clear from this information released by the DNI is that each of these programs is authorized by law, overseen by Congress and the courts and subject to ongoing and rigorous oversight,” said Sen. Mitch McConnell, R-Ky.

Zazi, an Afghan-American cab driver living in the Denver suburbs, was an al-Qaida-trained bomber. In September 2009, he sent a coded message to a Yahoo email address in Pakistan.

Months earlier, British officials had linked the Yahoo address to a known al-Qaida operative.

“The marriage is ready,” the email said in part.

The NSA intercepted that email, touching off a frenzied two-week investigation in New York and Colorado that led to Zazi’s arrest.

He pleaded guilty and provided information that helped send two friends to prison.