Mr. Christie has been trying to boost his stature by focusing on his experience as a prosecutor after the Sept. 11, 2001, attacks. He was first nominated for the position by former President George W. Bush the day before the attacks and used the Patriot Act to prosecute terrorism-related crimes as the state’s top prosecutor. He criticized Texas Sen. Ted Cruz and Mr. Paul for voting for legislation earlier this year to end a National Security Agency program to collect the phone records of millions of Americans.

Mr. Cruz recently accused Mr. Rubio of advocating “military adventurism.” Mr. Rubio Thursday took a veiled swipe back at Mr. Cruz, as well as Mr. Paul, for supporting legislation that would cut military spending and international aid. Without naming his Senate colleagues, Mr. Rubio took his rivals to task for opposing a bill authorizing funding for the “Iron Dome” missile shield that protects Israel.

“I believe those who speak about their pro-Israel views but carelessly support a gutting of our international affairs budget, including assistance to Israel, or who vote against legislation funding U.S.-Israel defense programs, need to check their priorities,” Mr. Rubio said. “You cannot be pro-Israel while also attempting to eliminate assistance that Israel uses to defend itself.”