The meeting was also attended by Gerhard Schindler, the head of Germany's BND intelligence service, and Hans-Georg Maassen, head of the Federal Office for the Protection of the Constitution.
They reported to the panel on talks held in Washington over the past days with US intelligence officials, partly about a proposed mutual "no-spy" agreement.
'Restore lost trust'
Ronald Pofalla, the head of the chancellery, said the planned agreement offered "a unique chance to regain the trust that had been lost," adding that the German delegations in Washington had gained the impression that the White House had "fully recognized" the political dimension of the spying affair.
Germany has expressed outrage after allegations, based on documents leaked by Snowden, that the US National Security Agency had tapped Chancellor Angela Merkel's mobile phone.
Pofalla said US President Barack Obama intended to inform the German government in mid-December about the results of the review he has ordered of the intelligence services. He added that cooperation between Germany and the US was to be placed on a "new basis" as part of the "no-spy" agreement.
Oppermann demanded that the proposed agreement also offer protection against excessive surveillance to normal citizens, and not just the German government.
Green politician Hans-Christian Ströbele, who visited Snowden in Moscow last Thursday, once more called on Germany to grant the whistleblower asylum. The government has repeatedly rejected such calls, saying that such a move would endanger the trans-Atlantic alliance with the US.