The 27 EU leaders are due to hold an emergency videoconference on the virus situation on Thursday
EU chief Charles Michel on Tuesday urged member states to adopt the quicker "antigen" coronavirus testing method, in coordination with their partners across the bloc.
In his weekly newsletter, Michel, the president of the European Council, said: "Within the space of just a few weeks, the situation has escalated from worrying to alarming.
"Now we must avoid a tragedy," he said.
To identify cases of Covid-19, European doctors have largely been using a "PCR test", which gives a result in days, rather than the quicker but less reliable "antigen" method.
Michel argued that, with a second wave of the epidemic "now upon us" it was time to move to the quicker test method.
"On a very large scale — that is to say, when the rate of infection is high — the system is difficult to manage," he said, of the PCR test, in which a nasal swab is sent for lab testing.
Michel said the technique should be backed up with "antigen tests, which — although currently regarded as less reliable — are more efficient, yielding results within 15 minutes."
But he warned, "we must not make the same mistakes as before: we must coordinate the approval of those tests in order to ensure that they are recognised Europe-wide."
When the coronavirus first arrived in Europe, some EU member states scrambled to secure stocks of protective equipment or close their borders, without waiting for Brussels' approval.
The 27 EU leaders are due to hold an emergency videoconference on the virus situation on Thursday.