By Jason Szep

ST. PETERSBURG, Florida (Reuters) - Republican presidential contender Mitt Romney often casts himself as an agent of change who would fix a "broken Washington" but he spares an obvious target -- President George W. Bush.

"I salute the fact the president has kept us safe these past six years," he told a rally on Saturday in Florida, whose primary on Tuesday is the next test in the most wide open race for the Republican presidential nomination in 50 years.

A day earlier, speaking to reporters, he was even kinder to the unpopular president, saying that while he differed with Bush at times he still deeply respects him.

"Has the president done everything perfectly? Absolutely not," he said. "But is he a person I deeply respect for his conviction and his appreciation for the country and his desire to do what's right for it? I sure do."

While Bush's job approval rating languishes near record lows of around 30 percent, it is more than double that among core Republican primary voters who could make the difference in Florida's primary.

Romney, a former Massachusetts governor, is aggressively courting that Republican Party base in his race with John McCain, a four-term Arizona senator who Florida polls show is neck-and-neck with Romney.

Florida is the next battle in the state-by-state contests to pick nominees for the November 4 presidential election to succeed Bush.

At campaign rallies, Romney presents himself as an outsider who would fix a "fundamentally broken" Washington. Both Democrats and Republicans, he often says, are to blame.