WASHINGTON — Iraqi and Kurdish ground troops overran Sunni militants and reclaimed Iraq’s largest dam on Monday, President Obama said, as American warplanes unleashed a barrage of bombs in an expansion of the limited goals laid out by the president in authorizing the military campaign in Iraq.

Mr. Obama, who interrupted a family vacation on Martha’s Vineyard to meet Monday with his national security team in Washington, maintained that the airstrikes around the Mosul Dam were within the constraints of what he initially characterized as a limited campaign meant to break the siege of stranded Yazidis on Mount Sinjar and protect American personnel, citizens and facilities in Iraq.

Administration officials repeatedly painted that second directive — the protection of Americans in Baghdad, 290 miles away — as the justification for the intense air campaign over Mosul Dam, seized two weeks ago by militants with the Islamic State in Iraq and Syria.

But such a definition gives the White House wide latitude to support Iraqi forces in a sustained military offensive against ISIS across the country. The president hinted that more help from the United States and international partners would come if Iraq’s Shiite majority governed in a more inclusive way.