KHARTOUM, Sudan — American commandos raced into Somalia early Wednesday and rescued two aid workers, an American woman and a Danish man, after a shootout with Somali pirates who had been holding them captive for months.

The American forces — drawn from the same Navy commando unit that killed Osama bin Laden — swooped in and killed nine pirates before spiriting away the hostages, who were not harmed, American officials said.

It appeared that President Obama was fully aware of the raid as he was about to give his State of the Union speech on Tuesday night, which would have been early Wednesday in Somalia.