Logar said the Chinese government should lift restrictions on movement and information.
"The EU stresses the importance it attaches to the right of freedom of expression and peaceful protest," Logar said.
Logar's comments echoed statements earlier on Tuesday by Condoleezza Rice, the US secretary of state.
Rice called on the Chinese government to open talks with the Dalai Lama, Tibet's spiritual leader, whom she said could play "a very favourable role" in dealing with the "grievances of Tibet".
Several days of anti-government protests led by monks spiralled into violence on March 14 in Tibet's capital, Lhasa.
The government said at least 22 people died in the city, while Tibetan rights groups say nearly 140 Tibetans were killed, including 19 in Gansu province.
Further protests were reported in Sichuan province on Tuesday, following clashes between demonstrators and police on Monday which reportedly left a policeman and at least one monk dead.
The continued Tibetan resistance and the hardline stance by officials has put China's human rights record under the spotlight and has frustrated the communist leadership, which had hoped for a smooth run-up to the August 8 to 24 Beijing Olympics.
Following the crackdown, Nicolas Sarkozy, France's president, said on Tuesday that "all options were open" regarding a possible boycott of the Beijing Olympics' opening ceremony.
During a visit to the Pyrenees region in the southwest of France, he said: "All options are open and I appeal to the Chinese leaders' sense of responsibility."
Aides to Sarkozy specified that France had not shut the door on a possible boycott of the opening ceremony on August 8, even though it still opposed any call to stay away from the entire games.
However, Germany, which has urged China and the Dalai Lama, to peacefully resolve the crisis, stressed on Tuesday that it did not back a boycott of the Olympics.
Thomas Steg, deputy spokesman for the German government, said: "We consider it essential that both sides, Tibet and the Dalai Lama on the one side and the government in Beijing on the other, move toward each other."
"The Tibetans want to protect their culture and China has an interest in stability and territorial integrity and thus the German government sees no alternative to a direct dialogue between the two sides."
Steg said Berlin stood by its position that an Olympic boycott would be counterproductive but renewed its call for China to practice "transparency" in Tibet by allowing foreign observers into the Himalayan region.
China has banned foreign journalists from traveling to the protest areas, making it extremely difficult to verify any information.
Last week, Germany suspended talks with China on development financing for renewable energy projects over its concerns about "the perpetuation of violence in Tibet."
The uprising is the broadest and most sustained against Chinese rule in almost two decades, and the communist leadership has accused the Dalai Lama and his supporters of masterminding the dissent.