The State Department has ordered Foreign Service officers in many nations to begin face-to-face interviews with millions of visa applicants who previously have not merited such scrutiny, a step that will result in months-long backlogs, according to officials and documents. The rules, formally issued in a cable sent to 221 embassies and consulates Wednesday, have prompted strong objections from business, education and tourism groups. The groups say that longer delays in obtaining visas will discourage foreign nationals from visiting the United States at a time when the economy is still struggling.