Abu Qatada was earlier freed from prison after a UK court ruled he might not get a fair trial if deported to Jordan to face bomb plot charges.
Mr Cameron said ministers had “moved heaven and earth” to try to deport him and would continue to do so.
Labour said people would be “horrified” and urged ministers to act quickly.
“We have moved heaven and earth to try and comply with every single dot and comma of every single convention to get him out of this country.
“It’s extremely frustrating and I share the British people’s frustration at the situation we find ourselves in,” Mr Cameron said.
He said that, as well an appeal, the government would “do everything we can to make sure that we do have the power to expel and deport people from our country who have no right to be there and mean us harm”.
As Deputy Prime Minister Nick Clegg vowed “we are absolutely determined to see this man get on a plane and go back to Jordan”, experts warned it could be months, even years before he leaves British soil.
Yesterday the Special Immigration Appeals Commission (Siac) ruled that it was not satisfied with assurances that evidence from witnesses who had been tortured would not be included in a retrial in his homeland and granted Qatada’s appeal, stating the Home Secretary was wrong not to revoke a deportation order.
The Government’s response is likely to be two-pronged. Theresa May has already stated that they will appeal on a matter of law. Meanwhile diplomatic efforts will undoubtedly be doubled to seek further assurances from the Jordanians.
Either option is expected to take time with any appeal unlikely before next year. The Home Secretary has three weeks to apply for permission for the matter to go before the Court of Appeal. If a single judge considering written submissions refuses the application, the Home Office can request an oral hearing before three appeal court judges.
A second option will be to make representations to the Jordanians after Siac said a key sticking point was an ambiguity in the country’s code of conduct, which led to the “real risk” that statement statements procured by torture would be admitted in a retrial.
The decision means that the security services and police will now have to watch him around the clock in a surveillance operation that is likely to cost the taxpayer more than £5 million a year.
Qatada is wanted in Jordan to face terrorism charges and featured in hate sermons found on videos in the flat of one of the September 11 bombers.