Egypt's Interior Ministry and security sources have said a preliminary investigation has revealed the man appeared to have swam from a nearby public beach in order to access the holiday resort.
Egypt's tourism industry, a main source of national income, has been in the doldrums since the 2011 uprising against long-time dictator Hosny Mubarak. The official spoke on condition of anonymity because he was not authorised to speak to the media.
Dozens of Christians have been killed in church bombings and shootings since last December in attacks claimed by IS.
Elsewhere on Friday, gunmen ambushed a checkpoint in Giza province south of Cairo, shooting and killing five policemen and setting their vehicle on fire.
Germany strongly condemned the attack on "people who only wanted to relax on the beach", but continued to assure it has issued no new travel warnings on Egypt.
Body of missing Cedar Hill woman found in Ohio
Harris was booked on charges of resisting arrest, obstructing official business and gross abuse of a corpse, jail records show. The body has not yet been positively identified, but authorities believe it is that of a missing woman from Cedar Hill, TX.
The Islamic State group (IS) claimed responsibility for the downing of a Russian passenger jet in 2015.
Tourists will keep on coming to Egypt, he argued, "because it's a cheap country with fantastic beaches and old heritage".
Hurghada is one of Egypt's most popular beach resorts, particularly with Ukrainians and other European tourists. They were only lightly wounded. Police officers shot and killed one of the assailants and wounded the other.
The Hasm, or "Decisiveness", is a militant group that authorities have linked to the now-outlawed Muslim Brotherhood.
Earlier on Saturday, the police similarly killed four militants in the Suez Canal city of Ismailia, confirming them as terrorists escaping from restive North Sinai. There was no claim of responsibility for that attack, either, and it was not clear whether the two incidents were connected. "They are not the ones wanted (targeted)".