Opposition lawmakers urged Rajoy to press the U.S. for explanations and to clarify if Spain had helped the NSA and whether he had any part in it.
Meanwhile, a German delegation met with American officials at the White House as part of Berlin's efforts to probe allegations that Chancellor Angela Merkel's cellphone was monitored by U.S. intelligence.
National Security Council spokeswoman Caitlin Hayden said in a statement that the dialogue focused on ways to "provide the necessary assurance" and "strengthen our cooperation," and that the U.S. looks forward to continuing the discussions.
The heads of Germany's foreign and domestic intelligence agencies also will visit Washington "in the coming days," said Merkel spokesman Steffen Seibert. He did not say who the Germans were meeting.
French officials were focused on "the nature and the extent of American spying on our territory," said Foreign Ministry spokesman Romain Nadal.
French government spokeswoman Najat Vallaud-Belkacem said that the facts "seem well established" and "from this point of view, the denials of the director of the NSA seem improbable."
Russian Foreign Minister Sergey Lavrov said his government wasn't surprised by reports of alleged U.S. monitoring of leaders of allied countries.
"I am persuaded that everyone knew everything or suspected everything," Lavrov said during a visit to Greece.
In Washington, Elmar Brok, a German member of the European Parliament and the current chairman of the European Parliament Committee on Foreign Affairs, told reporters at a news conference, "We want to get rid of espionage between friends."
Brok is leading a European delegation that is meeting with U.S. lawmakers and Obama administration officials on new revelations leaked by ex-NSA analyst Edward Snowden. The delegation expects to issue a report in February.
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Sylvie Corbet in Paris and Derek Gatopoulos in Athens, Greece, contributed to this report.