Another U.S. official said Obama, like every president, received detailed documents on the framework of the programs as part of his briefing when he took office in 2009.
One of the programs targeted leaders in specific countries, which would have been a focus of the briefing, according to the official.
Another senior administration official argued the president approves a set of intelligence priorities, and then it's the responsibility of his administration to determine how to carry those out, making it unreasonable to expect Obama to know every detail of exactly how that happened.
"I really doubt he had to sign off on something like that or get into the details," said a former senior administration official who worked on national security for the Obama White House.
To Feinstein, the fact that neither Obama nor her committee knew about the program was a "big problem."
"As far as I'm concerned, Congress needs to know exactly what our intelligence community is doing," her statement said. "To that end, the committee will initiate a major review into all intelligence collection programs."
White House: Reviewing surveillance of allies
Merkel said last week that reports of American spying on her and other leaders had "severely shaken" relationships between the United States and European nations.
The German leader said she told Obama last week that eavesdropping among friends "is never acceptable."
Carney repeated Monday the White House line that Merkel was not being monitored now and would not be in the future -- without saying whether she had been targeted in the past.
Also Monday, Sen. Susan Collins, a member of the Senate Intelligence Committee, said she knew of "no justification for the Administration's collection of intelligence on the leaders of our closest allies," such as Merkel.
"I will be seeing the German Ambassador tomorrow night and will express directly to him my belief that it was wrong for the Administration to engage in monitoring of the Chancellor's telephone calls," she said in a statement.
Should the president know wiretap details?
Separately, the NSA on Sunday denied a report by the German newspaper Bild am Sonntag that NSA Director Keith Alexander told Obama about the surveillance of Merkel in 2010.
"Gen. Alexander did not discuss with President Obama in 2010 an alleged foreign intelligence operation involving German Chancellor Merkel, nor has he ever discussed alleged operations involving Chancellor Merkel," NSA spokeswoman Vanee' Vines told CNN.
German intelligence officials are scheduled to meet with their American counterparts in Washington this week to ask about surveillance programs.
Other news media reports, based on documents leaked by Snowden, have said the NSA monitored the communications of the leaders of Brazil and Mexico.
Germany and Brazil are drafting a United Nations resolution on privacy in electronic communication, officials in those countries said last week.
Report: NSA monitored 60 million Spanish calls in 30 days
The Spanish newspaper El Mundo reported Monday that the NSA collected data from 60 million phone calls in Spain in one 30-day period.
One of the authors of the El Mundo article was Glenn Greenwald, the journalist who first reported on documents supplied by Snowden for the British newspaper The Guardian.
The El Mundo article cited what it said was an NSA report titled, "Spain -- last 30 days." The 60 million calls were not recorded, but the NSA collected serial numbers of devices, phone numbers, locations and durations of calls, the newspaper said.
In an interview Monday with CNN, Greenwald denied assertions by U.S. officials that the surveillance program was purely for security reasons.
"None of this has to do with terrorism," he said. "Is Angela Merkel a terrorist? Are 60 or 70 million Spanish or French citizens terrorists? This is clearly about political power and economic espionage and the claim that this is all about terrorism is seen for what it is all around the world, which is pure deceit."
Carney denied any economic motivation, telling reporters that "we do not use our intelligence capabilities for that purpose."