The New York Times has reported that James Comey, a deputy to then Attorney-General John Ashcroft, refused to extended the NSA program in 2004.
White House aides then appealed to Mr Ashcroft while he was in hospital for gallbladder surgery, the Times said.
"This NSA program is an important program protecting Americans," Mr Bush said after visiting wounded troops at Brooke Army Medical Centre in San Antonio, Texas. "We're at war."
Mr Bush said the program was limited to "a few numbers" called by known al-Qaeda members outside the United States.
"If somebody from al-Qaeda is calling you, we'd like to know why," Mr Bush said.
However, Democratic Senator Charles Schumer, a member of the Judiciary Committee, said he would ask committee Chairman Arlen Specter to seek testimony from Mr Comey, Mr Ashcroft, Attorney-General Alberto Gonzales and White House Chief of Staff Andrew Card.
"Today's revelations really heighten concerns about this. When (James) Comey, who was one of the premier terrorism prosecutors in this country, said that he thought this program violated the law... it calls into question to way the president and the vice president went about changing it," Senator Schumer said on Fox News Sunday.
The New York Times reported two weeks ago that Mr Bush authorised the NSA to monitor, without court approval, the international telephone calls and emails of US citizens suspected of links to foreign terrorists.
A 1978 law, the Foreign Intelligence Surveillance Act, makes it illegal to spy on US citizens in the US without the approval of a special court.
Senator Schumer said if the president thought the law hampered the war on terrorism he should have asked Congress to consider making changes.
"Unilaterally changing the law because the vice president or the president thinks it's wrong, without discussion, that's not the American way," Senator Schumer said.
The Bush administration has argued the eavesdropping is legal and said congressional leaders were told of the program.
Mr Bush said on Monday that the program was being "constantly reviewed by people throughout my administration".
Republican Senator Mitch McConnell said on Fox News Sunday that
Congress should focus on investigating who in the US government leaked the existence of the program to the Times.
The Senate Intelligence Committee, which often meets in closed session, would be a better place than the judiciary panel to investigate the program, Senator McConnell said.
According to the Times report, Mr Comey's refusal to reauthorise the NSA program prompted Card and Gonzales to try to get the needed approval from Ashcroft in March 2004 while he was in a Washington hospital for gallbladder surgery.