"We're going to have to stay engaged because these people still want to kill Americans, and so the war on terror is going on," Grassley says. "The only thing the president announced yesterday is the phases in Iraq and Afghanistan are soon over."

Several Republicans on Tuesday criticized Obama for appearing to use Afghanistan as a backdrop to remind voters of bin Laden's death in the run-up to the November elections. Grassley did not repeat that complaint, but did say he opposes making it clear to America's enemies what the next moves are militarily.

Obama signed an agreement in Kabul cementing a long-term relationship with Afghanistan after U.S. troops leave in 2014, which gives the United States the ability to keep some troops there.

"The only qualms I have about anything the president said is emphasizing to our enemies exactly what our next military move is, or the lack of a military move," Grassley said. "I don't like sending signals to the enemy when we're going to do it and setting deadlines."

Grassley on Wednesday also tweeted, "PresO peace in afghanistan is not end of war on terror. That war started three decades b4 BIN LADEN and it will go on decades aft BinLaden."