Reding said that if the country was able to enact legislation virtually overnight just before the accession, it should also be able to revise it within days.
The law officially is intended to protect veterans of its 1991-95 war for independence from prosecution abroad. Critics say that, in fact, it is intended to protect a former Croatian intelligence chief sought by Germany in the murder of a Croatian dissident.
Perkovic, who created Croatia's secret service once the nation split from the former Yugoslavia in the 1990s, worked for the Communist Yugoslavia's secret service in the 1980s.
Milanovic insisted that Croatia was not trying to protect anyone, but needed more time because the issue was sensitive for the country.
President Ivo Josipovic, however, adopted a more conciliatory tone, urging for changes to the law "as soon as possible."
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Jovana Gec in Serbia and Juergen Baetz in Brussels contributed.