Washington and Berlin are also working on a no-spying agreement, with talks set to start later this month, said the chancellery chief of staff who oversees German secret services, Ronald Pofalla.
"The US and British intelligence services have assured us that they respect the law in Germany," Pofalla said after a closed-door parliamentary oversight committee hearing.
He also told the media, without taking questions, that "in Germany there is no million-fold violation of the basic law".
The claims made by fugitive former US intelligence analyst Edward Snowden about mass online data surveillance by US and British intelligence services have sparked wide consternation in Germany.
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As political parties wage battle ahead of September 22 elections, government and secret service figures have repeatedly faced the parliamentary oversight committee in closed-door meetings.
The chairman of the committee, the opposition Social Democrat Thomas Oppermann, said meanwhile that the more than five-hour meeting had failed to shine much light on the affair.
He said the panel therefore "continues to call on the chancellor to demand from the United States the transparency that (President Barack) Obama has promised".