WASHINGTON — The United States, as promised by President Obama, has stepped up its airstrike campaign in Iraq, hitting targets near Baghdad in the effort to help the Iraqi government win back territory seized by the Islamic State in Iraq and Syria, Pentagon officials said Monday.

The offensive is the first expansion of the United States’ campaign against the Islamist militant group that Mr. Obama outlined last week in a speech to the nation.

The new campaign included a strike on Monday southwest of Baghdad and one the day before near Sinjar, Iraq, the Defense Department said in a statement. The strikes, the Pentagon said, go beyond the United States’ initial mission announced last month of “protecting our own people and humanitarian missions.”