WASHINGTON — Congressional Republicans increasingly reject any use of the civilian criminal justice system for handling cases involving Al Qaeda, hardening their stance in a dispute with the Obama administration over whether such suspects should be held and prosecuted exclusively by the military.

Republican senators are pushing to include a provision in a 2012 military authorization bill that would require Qaeda suspects accused of plotting attacks and who are not American citizens to be held in military custody — even people arrested in the United States. The White House opposes such a blanket rule.

Amid negotiations over the bill, Republicans — who see their position as a potent election issue in 2012 — delivered an overwhelming show of unity in support of such ideas late last week, as 45 of the party’s 47 senators voted for a similar proposal to ban civilian trials for such “enemy combatants.” The endorsement highlighted a drastic shift to the right in the politics of counterterrorism since President Obama succeeded George W. Bush.

Mr. Bush used the criminal justice system for some cases and the military system for others, as has Mr. Obama. In recent years, the once-fierce criticism from liberals about the legitimacy of any use of military detention and tribunals has become muted. Meanwhile, Republicans, who accepted the hybrid approach under Mr. Bush, increasingly reject any use of the civilian system.