The meeting comes just hours after Mr Clapper and Gen Alexander testified before the intelligence panel of the House of Representatives on Tuesday.
Gen Alexander said much of the data cited by non-US news outlets was actually collected by European intelligence services and later shared with the NSA.
Meanwhile, Mr Clapper told lawmakers that discerning foreign leaders’ intentions was “a basic tenet of what we collect and analyse”.
He said that foreign allies spy on US officials and intelligence agencies as a matter of routine.
Mr Clapper said the torrent of disclosures about American surveillance had been extremely damaging and that he anticipated more.
But he said there was no other country that had the magnitude of oversight that the US had, and that any mistakes that had been made were human or technical.
The BBC’s Jonny Dymond in Washington says if anyone was expecting apologies or embarrassment from the leaders of America’s intelligence community, they were in for a disappointment.
The intelligence pair were not given a tough time by the committee but that sentiment is turning within Congress toward tightening up the reach of American intelligence agencies, our correspondent says.
Meanwhile, the spokesman for Russian President Vladimir Putin has denied that Moscow used free USB memory sticks and mobile phone charging cables to spy on delegates attending the G20 Summit in St Petersburg last September.
Reports in two Italian newspapers suggested that the USB sticks and cables had bugs on them that could steal data from the delegates.
Spokesman Dmitri Peskov said the reports were an attempt to distract from the problems between European countries and the US.