Bush also praised McCain for backing his Iraq "surge" policy and said the former naval pilot who spent years in Vietnam as a prisoner of war would not have his resolve broken by "the angry left".
American security depended on McCain's election, Bush said.
"We live in a dangerous world," Bush said. "And we need a president who understands the lessons of September 11, 2001: that to protect America, we must stay on the offence, stop attacks before they happen, and not wait to be hit again. The man we need is John McCain."
Less of Bush
Bush had been scheduled to address the convention on its first day but cancelled, giving the reason that he wanted to be closer to hurricane preparations in Texas.
The president addressed the convention on Tuesday for just a few minutes, a move representing a carefully orchestrated compromise with McCain's camp in a reflection of the delicate balancing act the Republican candidate faces as he looks to distance himself from the incumbent president.
More prominent speaking roles on Tuesday went to Joe Lieberman, the Democrats' vice-presidential candidate in 2000 and now an independent senator, and Fred Thompson, the former actor and rival to McCain who dropped out of the presidential race earlier this year.
'Independent' Democrat Lieberman is backing McCain [GALLO/GETTY]
Joe Lieberman, a close McCain ally, described Barack Obama, the Democratic presidential candidate, as a "gifted and eloquent young man," but said "eloquence is no substitute for a record, not in these tough times".
"I'm here to support John McCain because country matters more than party," said Lieberman.
Aides said McCain would probably deliver his nomination acceptance speech in person as scheduled on Thursday.
McCain announced Alaska's governor Palin - largely unknown nationally - as his running mate last week, which fuelled talk that adequate research was put into his vice-presidential selection.
Palin, the 44-year-old mother with a reputation of being a maverick, announced hours before the convention began on Monday that her unmarried 17-year-old daughter was pregnant.
A legislative committee in her home state disclosed on Monday that Palin had hired a lawyer to represent her in an investigation into whether she abused her power when she fired a state official for allegedly personal reasons.
McCain said on Tuesday that he was satisfied that Palin's background was properly checked, telling reporters as he toured a Philadelphia, Pennsylvania, fire house that the "vetting process was completely thorough and I'm grateful for the results".
The man who led McCain's vice-presidential search team, Arthur Culvahouse Jr, said he thought everything that had come up as a possible red flag during the background check had now been made public.
Palin is expected to address the convention on Wednesday.
Outside the Xcel Energy Centre, about 2,000 people protested against poverty and homelessness on Tuesday.
Protesters in Minnesota have accused police of being heavy-handed [AFP]
Police officers were out in force, many in full riot gear, and said they were ready for trouble a day after nearly 300 people were arrested for scattered acts of violence near the arena.
Police blamed a splinter group of about 200 for harassing delegates, smashing windows, puncturing car tyres, throwing bottles and starting at least one fire after about 10,000 people had held a largely peaceful anti-war march.
Protesters countered that police were heavy-handed, after several journalists were also detained and pepper spray was used on some marchers on Monday.
Gustav, weaker than expected, hit the heart of Louisiana's oil and fishing industries but appeared to spare New Orleans the catastrophic flooding of Katrina.
Still, its political impact was unclear. For a day at least, the storm denied McCain the non-stop news coverage that Obama enjoyed during the Democratic convention in Denver, Colorado, last week.
Obama also scaled back his political activities and turned his attention to the Gulf coast region, urging supporters to donate to the American Red Cross.