Paul was set to address a gathering of gun enthusiasts in Las Vegas before flying to Minnesota, where he will campaign ahead of that state's caucuses on Tuesday.
Santorum was in Missouri, which holds a non-binding contest Tuesday. Gingrich is not on the ballot there.
To that end, Santorum cast Gingrich's effort as a decaying campaign and said that the former House speaker's decision to stay in the race was only helping Romney.
"With Speaker Gingrich out of the race, almost all of the votes he has go to me," Santorum said in Hannibal, Mo., pointing to the upcoming Missouri contest as a chance to illustrate his point. "When we go head to head with Gov. Romney, we can beat him."
Associated Press writers Philip Elliott in Hannibal, Mo., and Beth Fouhy in Pahrump, Nev., contributed to this report.
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