The three patients in the EU confirmed to have the virus — one in Spain and two in Britain — are recovering well.
The suspected cases are in Ireland, Denmark, Sweden, Greece, Germany, the Czech Republic and Italy.
The European Commission’s health chief, Androulla Vassiliou, said she expects the situation to change in the EU over the next few days as an increasing number of cases are confirmed.
She has called an urgent meeting of pharmaceutical industry representatives to discuss the state of flu treatments and a vaccine.
Ms Vassiliou said the union had not yet formally advised that travel should be banned.
The US has warned people against travelling to Mexico where the death toll is rising, and EU health ministers, meeting in emergency session tomorrow, are expected to issue similar warnings.
Ms Vassiliou said they want to change the name of the flu from swine flu to novel flu, because people were becoming confused and believed they could contract it from eating pork. However, this was not possible provided the pork was cooked, she added.
The name, novel flu, reflects the fact that the strain is much different to other flus as the virus contains pig, bird and human genes.