An explosion in the city centre early on Saturday targeted US military personnel, said US military spokesperson Captain Tim Crowe. Another five soldiers were injured.
A US officer in Baghdad described the incident as a complex attack involving a roadside bomb backed up by small arms fire.
He said some of the wounded had sustained life-threatening injuries. No arrests were reported.
Tikrit is the hometown of former Iraqi president Saddam Hussein.
Added to an official Pentagon tally, the deaths raise to 270 the number of US soldiers killed in action since US President George Bush declared official hostilities over on 1 May last year.
Meanwhile, in Baghdad a bomb rocked a shop in a busy commercial district, killing the brother-in-law of a member of the US-led occupation's Iraqi Governing Council.
Iraqi police confirmed one man was killed and another was wounded in the explosion. An aide to Ibrahim al-Jaafari, a Shia council member, identified the slain victim as Haidar al-Qazwini and said he was al-Jaafari's brother-in-law.
Police said an unidentified man had entered the shop in the Karrada neighbourhood earlier and left a bag containing explosives.
Al-Jaafari is the main spokesman for the Islamic Dawa party, which was once based in Iran.
Also on Saturday, the US announced it would introduce a new border policy to try and keep out "foreign insurgents", including closing off most of the official crossing points from Iran.
The new policy had been formulated in conjunction with the Iraqi Governing Council and Interior Ministry, a senior US official said.
The US will tighten security on the
Just three of more than 10 official entry points from Iran would remain along the nearly 1500km frontier.
US officials say there is an increasing threat from foreign fighters in Iraq, who they believe are behind some of the major bombings of recent months.
After near-simultaneous attacks this month killed more than 180 people in Baghdad and Karbala, the occupation administrator in Iraq Paul Bremer made a statement reiterating that Washington had committed $60mn to border security.
After those attacks, the top Shia cleric in Iraq criticised the US for not doing enough to police borders and protect the country it is occupying.
US authorities in Iraq had previously indicated the focus
of border controls would be the Iranian and Syrian borders.