In his weekly radio address, Mr. Bush said his eventual nominee will be a "fair-minded individual who represents the mainstream of American law and American values."
His candidate also "will meet the highest standards of intellect, character and ability and will pledge to faithfully interpret the Constitution and laws of our country," the president said.
"Our nation deserves, and I will select, a Supreme Court justice that Americans can be proud of," he said, without revealing the name that many are anxious to hear.
Mr. Bush also discussed his recent meeting with Senate leaders of both parties to discuss the nomination and confirmation process for a replacement for Sandra Day O'Connor. The first woman to serve on the high court, O'Connor announced July 1 that she is stepping down after 24 years.
Much of the retirement speculation — before and after O'Connor's surprise announcement — had focused on Chief Justice William H. Rehnquist, who is 80 and ailing with thyroid cancer.
Rehnquist tried to dampen expectations this week, issuing a statement in which he said his retirement is not imminent and that he would continue on the court "as long as my health permits."
While the expected battle over the Supreme Court is Topic A in Washington, Mr. Bush also said he is working on "other important priorities" while reviewing the dossiers of potential nominees.
He noted the week's positive economic news — this year's budget deficit is expect to come in nearly $100 billion below previous estimates — and reflected on his pledge to cut the deficit in half by 2009.
"This week's numbers show that we are ahead of pace, so long as Congress acts wisely with taxpayer dollars," Mr. Bush said. He also noted recent signs of economic growth and a 5 percent unemployment rate.
But the president also prodded Congress to make progress in several areas that he said will keep the economy growing and creating jobs, including by finishing work on:
He also pressed for action on his proposal to overhaul Social Security for younger workers.
Bush said he and Senate leaders agreed on the need for a dignified confirmation process for his Supreme Court choice. He noted the treatment of President Clinton's nominees — Ruth Bader Ginsburg and Stephen Breyer — as examples of how it has been done.
In 1993, the Senate voted on Ginsburg 42 days after Clinton submitted her nomination. Despite philosophical differences with some senators, she was confirmed by 96 of the 100 members.
A year later, Breyer's confirmation came 73 days after his nomination, and he received 87 votes.
"These examples show that thorough consideration of a nominee does not require months of delay," he said, and repeated his intention to make an announcement in time for the person to be confirmed before the court's new term begins in October.