US adopts 'aggressive' approach in Iraq
American soldiers backed by armoured vehicles and helicopters also raided a Baghdad neighbourhood overnight.
US commanders are adopting what they call a "more aggressive" approach in response to mounting losses.
President George W Bush has admitted last week was tough but said: "We're going to deal with the terrorists."
His forces were changing their tactics to match those of their enemies, he said.
Early on Monday, witnesses near Tikrit reported the ground shaking as flares lit up the night sky.
US troops shelled positions from where they believe insurgents had fired mortars or rockets on their base in Tikrit.
"For us, this is not a display. We want to get the enemy...The message is 'Give up, it's over'," Lieutenant-Colonel Steve Russell said.
The bombardment was part of Operation Ivy Cyclone Two which is targeting insurgents in north-central Iraq.
It comes after 17 coalition troops died when two Black Hawk helicopters collided and crashed in the northern city of Mosul on Saturday - one was reportedly hit by ground fire.
US forces fired a satellite-guided missile at a "guerrilla camp" about 25km (15 miles) west of Kirkuk on Sunday, for the first time since major combat ended.
Pressure is also being stepped up in the Iraqi capital where American forces moved into the upper-class Sunni Muslim neighbourhood of Azamiyah, searching 450 houses over seven hours in the hunt for weapons and fighters.
The raids angered many residents.
"Of course everybody has weapons. We have all been robbed. We were afraid of the Iraqis and now we're afraid of the Americans," said Samir al-Hadith, an engineer from Saudi Arabia living in the neighbourhood.
US forces are clearly on the offensive in Iraq in the face of mounting casualties among coalition troops and the loss of five helicopters in just over three weeks, the BBC's Peter Biles in Baghdad says.
The operation in Tikrit took place hours after an Arabic TV station broadcast an audio tape purported to be of the ousted Iraqi dictator.
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