ATLANTA  President Obama on Monday opened a monthlong drive to mark the end of the combat mission in Iraq and, by extension, to blunt growing public frustration with the war in Afghanistan by arguing that he can also bring that conflict to a conclusion.

The series of events, starting with a speech here to a veterans’ group, puts the president in the thick of a volatile national security debate at a critical moment for both wars as he draws down troops from one theater and sends more to the other. While seeking to shore up domestic support, he is also defining the limits of his ambitions in both Iraq and Afghanistan.

Mr. Obama vowed to complete his plan to withdraw designated combat forces from Iraq by the end of August “as promised and on schedule,” even though a political impasse has left Baghdad without the permanent government that his strategy originally envisioned. At the same time, he vowed to destroy Al Qaeda in Afghanistan while sticking to “clear and achievable” goals rather than aspiring to build a fully functioning democracy.

The president’s renewed public focus on the wars comes after many months in which his domestic agenda was at the center of the national conversation. But the White House calculated that the drawdown in Iraq and the change in mission there this month provided an opportunity to take credit for fulfilling one of Mr. Obama’s central campaign promises even as war fatigue takes its toll.