Snow died of colon cancer Saturday at age 53. He is survived by his wife, Jill, and their three children.
The president described Snow as a smart, capable man of good values. Bush said that he and first lady Laura Bush offered Snow's family his prayers.
"I just hope they understand that Tony was loved here in the White House," Bush said with his wife by his side.
Snow was the White House press secretary from May 2006 until last September. He long was a member of Washington's power circles, and a familiar face across the country, as a conservative commentator and an interviewer on TV and radio for Fox News.
Snow also served in the first Bush administration as speechwriting director and later as a deputy assistant to the president for media affairs.
Before he became press secretary, Snow had his colon removed and had six months of chemotherapy after being diagnosed with cancer. Then, in 2007, his cancer returned. He had more surgery and returned to work, remaining in good spirits while enduring chemotherapy.
In his comments before the television cameras Sunday, Bush echoed his written statement of a day earlier, when he praised Snow for wit and grace.
Other White House figures spoke up to honor Snow, too.
Presidential counselor Ed Gillespie said that Snow's jousting with reporters in the White House briefing room was always fun to watch. "I always said that Tony Snow's briefings could air not only on C-SPAN but on pay-per-view," Gillespie said "Face the Nation" on CBS.
Vice President Dick Cheney, in an interview on the "Fox News Sunday" show that Snow once hosted, said Snow was the best press secretary he had known in 40 years in Washington.