"The program's legal, it's designed to protect civil liberties, and it's necessary," Mr. Bush said.
On the Middle East, Mr. Bush said Wednesday's Palestinian vote shows the Palestinian people want change, but he won't change his stance on Hamas, CBS News correspondent Peter Maer reports.
Mr. Bush said that any organization that has an armed wing and which advocates violence against Israel "is a party with which we will not deal."
"If your platform is the destruction of Israel, it means you're not a partner in peace, and we're interested in peace," Mr. Bush said.
Democrats have accused the president of breaking the law in allowing eavesdropping on overseas communications to and from U.S. residents, and even some members of his own party have questioned the practice.
A newfound 61 percent of Americans believe the eavesdropping program is meant to fight terror, while 29 percent believe it is an attempt to expand the powers of the presidency. The poll also found that 53 percent of Americans approve of the program and 46 percent do not.
CBS News chief White House correspondent John Roberts reports the president insisted again Thursday he is on solid legal ground, and was skeptical about increasing talk in Congress to write new laws covering the program.
"It's so sensitive that if information gets out about how the program works, it will help the enemy," Mr. Bush said. "Why tell the enemy what we're doing?
"We'll listen to ideas. If the attempt to write law is likely to expose the nature of the program, I'll resist it."
After the news conference, Democratic Sen. Richard Durbin of Illinois said Mr. Bush is off-base when he claims he has legal authority for domestic eavesdropping because of the war on terror.
As part of what Democrats billed as a "pre-buttal" to next week's State of the Union, Durbin said "the president has the responsibility to come forward and tell us if the law needs to be changed. Neither this president nor any president is above the law."
It was the president's first full-scale news conference of the new year, and the 10th since he was re-elected in 2004. He previewed his State of the Union address and fielded questions on former lobbyist Jack Abramoff,in Palestinian elections, and the administration's cooperation with Congress on its investigation of Hurricane Katrina.
Mr. Bush called the election results a "wake-up call" to the old-guard Palestinian leadership, many of whom are holdovers from the days of the late PLO chairman Yasser Arafat.
Questioned about the controversy swirling around Abramoff, Mr. Bush said he would cooperate with federal prosecutors investigating Abramoff and his alleged influence peddling, if necessary. Otherwise, the president said he saw no reason to release pictures that he acknowledged were taken of him and Abramoff.
"There is a serious investigation going on by federal prosecutors — that's their job," the president said. "If they believe something was done inappropriately in the White House, they'll come and look and they're welcome to do so."
Otherwise, Mr. Bush said, "I've had my picture taken with a lot of people. Having my picture taken with someone doesn't mean I'm a friend with them or know them very well."
"I've had my picture taken with you," Mr. Bush said to CBS News White House correspondent Mark Knoller, who asked the question.