It is not remarkable that the government paid the companies for their costs. In the 2008 law, Congress required compensation “at the prevailing rate” to electronic communications service firms for “providing information, facilities or assistance” in complying with surveillance directives.

But it is not clear why Prism providers would incur significant extra costs for the mere extension of the expiration date for the older set of procedures already in use — especially when the problem leading to the delays in approving new certifications involved an issue only on the upstream surveillance operation.

An earlier internal N.S.A. newsletter leaked by Mr. Snowden, and made public last week by The Washington Post, appeared to conflict with the October 2012 newsletter. The earlier document, written shortly after Judge Bates’s ruling in October 2011, said that Prism was not affected by his decision to allow the upstream collection to continue only for a month if the problems were not fixed. Most Prism companies had already been “transitioned” to new annual certificates, it said, with the last two — Google and Yahoo — expected to complete that step soon.

Both the N.S.A. and several tech companies declined to explain the apparent discrepancy about whether the extensions and delays affected e-mail companies involved in the Prism program, nor — assuming they did — say why the costs would be significant.

Google has rejected reports that it knowingly participates in Prism. It has asked the government for permission to say more about how they provide personal data about foreign users in response to surveillance court orders.

In a statement on Friday, Google reiterated that it has “not joined Prism or any government surveillance programs” and said it wanted to say more to the public. But it declined to answer questions about the fall 2011 episode.

Yahoo also declined to answer specific questions about how recertification works, saying only: “Federal law requires the U.S. government to reimburse providers for costs incurred to respond to compulsory legal process imposed by the government. We have requested reimbursement consistent with this law.”