A furious dispute over missed deadlines has broken out between London and Strasbourg after the European court of human rights halted an attempt to deport the radical Islamist cleric Abu Qatada less than 24 hours after it was ordered by the home secretary.

Theresa May ordered Qatada's arrest and detention on Tuesday in the belief that the three-month deadline for appeals to be lodged against the original Strasbourg ruling on the case on 17 January had passed at midnight on Monday.

But it emerged on Wednesday that Qatada's lawyers had lodged an 11th-hour appeal on Tuesday night, halting moves by the Home Office to press ahead with the deportation proceedings.

The development, which comes on the eve of the British-organised prestigious Council of Europe conference in Brighton to reform the working of the European court of human rights, is embarrassing to the home secretary.

May told the Commons on Tuesday that Qatada could be sent back to Jordan "in full compliance with the law".

But a European court of human rights spokeswoman said that the ECHR believed the deadline was midnight on Tuesday, and not Monday night as was assumed by the Home Office. She said this meant the legal block on the radical cleric's deportation to Jordan remained in force until a panel of European judges decided whether the case should go to the court's grand chamber on appeal.

"We did receive a referral to the grand chamber from the applicant at 11pm and it will be decided by a panel of judges at a date to be fixed," she said.

The Home Office strongly disputes this, insisting the deadline for appeals had expired, lifting the "rule 39" injunction and finally clearing the way for his deportation.

"Qatada has no right to refer the case to the grand chamber of the European court of human rights, since the three-month deadline to do so lapsed at midnight on Monday night. His case should be heard in British courts, as the home secretary outlined to parliament yesterday. In the meantime, he remains in custody," said a Home Office spokesman.

A Strasbourg spokeswoman said: "It is always open to the other party in the case to argue that a referral request is not made within the time limit.

"One of the questions that the grand chamber panel will have to decide is whether the request was sent within the time limit set out in article 43 of the convention.

"We cannot comment on the view taken by the UK authorities about when the deadline expired."

Article 43 adds that the three calendar months are not interrupted by bank holidays.

May claimed the last-minute appeal was no more than a delaying tactic by Qatada's lawyers and insisted it was out of time.

"There is no question that we have broken the law in arresting Abu Qatada. I am absolutely sure we got the deadline date correct," she said.

"We believe the appeal is outside the deadline. His lawyers only decided to lodge this appeal after they saw the strength of our case at the special immigration appeals commission to resume his deportation to Jordan." She said that once the issue was resolved the deportation proceedings would be resumed. "I don't think anybody should be surprised at the use of these delaying tactics," she said.

David Cameron said he was still determined to expel Qatada. The prime minister said on Wednesday evening: "I am absolutely clear, the entire government is clear, and frankly I think the country is clear, that this man has no right to be in our country.

"He is a threat to our security, he has absolutely no further call on our hospitality and he should be deported. That is what we are determined to achieve, no matter how difficult it is, no matter how long it may take."

Yvette Cooper, the shadow home secretary, said: "The home secretary needs to urgently come back to parliament to tell the public what on earth has happened here.

"The Home Office are saying one thing, the European court another. Why didn't they just agree the deadline in advance so there could be no opportunity for Abu Qatada or his lawyers to exploit?

"We said to Theresa May yesterday that there seemed to be a troubling level of confusion over this process, and so it has proved."

Cooper added: "We need urgent clarification from the home secretary on whether she got the timing wrong and why checks were not made with the ECHR, whether Abu Qatada may now be released because of a government mistake, and what is happening now to ensure this process is put back on track."

Keith Vaz, the chairman of the Commons home affairs select committee, said Qatada's deportation was becoming "chaotic and almost farcical".

He said: "It's very important that [May] should clarify this as soon as possible by making a statement to the house after she knows what the facts are."

The Conservative backbencher David Davis said the fresh block on Qatada's deportation was embarrassing for the home secretary. He said he did not blame May but said the Home Office had "dropped the home secretary and her ministers in it". The former shadow home secretary said he hoped Qatada was not released on bail but remained in custody in maximum security conditions.The Labour justice spokesman Chris Bryant said it showed May had failed to check all the relevant details in the runup to Qatada's arrest.

"All of us want Abu Qatada to be deported to Jordan; we also want the home secretary to go through the proper processes, abide by the law so we don't end up having to pay compensation to this ghastly man – but what seems to have happened is that the very basic details weren't done before the big fanfare of the announcement yesterday."