UK warns Iran after embassy stormed
Offices were ransacked and flags burned in the attacks, which followed a demonstration against sanctions imposed on Iran over its nuclear programme.
Mr Cameron described the attacks as "outrageous and indefensible".
The US and EU also condemned the attacks. Iran's foreign ministry expressed "regret" for the incidents.
The demonstrations followed a vote in Iran's parliament to reduce diplomatic ties with Britain in retaliation for imposing further sanctions.
'Dangerous situation'
Mr Cameron said the failure of the Iranian government to defend British staff and property was "a disgrace".
He said all British staff and their dependents had been accounted for and he praised Britain's ambassador to Iran, Dominick Chilcott, for handling a "dangerous situation with calm and professionalism".
"The Iranian government must recognise that there will be serious consequences for failing to protect our staff. We will consider what these measures should be in the coming days," he added.
US President Barack Obama said he was "deeply disturbed" by the attack.
"That kind of behaviour is not acceptable, and I strongly urge the Iranian government to hold those who are responsible to task," he said.
Germany, France and the EU also condemned the attack.
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