In a separate statement the bloc's presidency said it was very concerned by violations of the rights of the Kurdish minority in Iran and by death sentences passed on five members of the ethnic group.
Both statements were published as the United States and Britain said major powers had agreed on Wednesday to consider more U.N. sanctions on Iran after Tehran gave no concrete reply to their demand that it freeze its nuclear activities.
Arash and Kamiar Alaei are brothers who specialize in the treatment of HIV/AIDS and were arrested on June 21 and 22.
The U.S. State Department has expressed its concern, and rights groups Amnesty International and Physicians for Human Rights have called for the pair's release.
"The Presidency of the Council of the European Union calls on the Iranian government to immediately release Arash and Kamiar Alaei and to drop all charges that might be brought against them," France, which holds the EU's rotating six-month presidency, said in a statement.
"In their latest statements, the Iranian authorities have without any foundation accused the Alaei brothers, who are internationally recognized for their work in the prevention and treatment of HIV/AIDS in Iran, of participating in activities to destabilize the Islamic Republic," the Foreign Ministry said.
It did not elaborate on the substance of the accusations.
Western diplomats and human rights group say Iran has cracked down on dissenting voices since President Mahmoud Ahmadinejad came to power in 2005 on a pledge to revive values of the Islamic revolution launched almost three decades ago.
The diplomats and rights groups say pro-reform students, women's rights activists and labor activists are among those targeted in the clampdown, which they say could be in response to Western pressure on Iran over its nuclear program.
In a statement on the Kurdish minority in Iran, the EU Presidency said: "the EU is very concerned by the violations of the rights of some of the people of the Iranian province of Kurdistan by the Iranian authorities.
"It is with great concern that the EU learnt of the condemnation to death of Farzad Kamangar, Farhad Vakili, Ali Heidarian, Hivar Botimar and Anvar Hosein Panohi,"
Amnesty International said last month that abuses against Kurds had intensified in recent months with courts sentencing members of the ethnic group to death or lengthy imprisonment following flawed trials.
The United States accuses the Islamic Republic of seeking to build nuclear bombs. Tehran denies the charge.
(Reporting by Francois Murphy in Paris and Ingrid Melander in Brussels)
