The EU has been accused of supporting the Tunisian "structures of dictatorship".
French green MEP Daniel Cohn-Bendit accused the EU of being "scared" of challenging the regime of the ousted president Zine al-Abidine Ben Ali, during a debate on 17 January 2011.
New protests have broken out on the streets of Tunisia's capital, Tunis, as a new national unity government was announced.
President Ben Ali, who had been in power for 23 years, fled to Saudi Arabia on Friday after a month of mounting protests across the country over unemployment, food price rises and corruption.
Disturbances have been ongoing since mid-December, when a young unemployed graduate killed himself after a dispute with local officials who had prevented him from selling vegetables in the streets.
Protests against the country's unemployment issues have spread across the country, leading to a violent crackdown by the authorities.
Opening the debate, Parliament president Jerzy Buzek praised the "determination and courage" of the Tunisian people and called on the authorities to immediately released everyone detained in the protests.
He said there needed to be an independent inquiry into corruption and violence and urged free and fair elections.
The Commissioner for EU Neighbourhood Policy Stefan Fule told MEPs that any future "enhanced status" for Tunisia on trade relations had to ensure greater protection of fundamental rights.
Read Democracy Live's guide to how the plenary sessions work