The EU statement stressed that both sides of the conflict should respect human rights and international humanitarian law.
The EU presidency went on to welcome the announcement by UN Secretary-General Ban Ki-moon that the United Nations will do whatever it can to support a pause in military operations and help improve the situation for civilians in the conflict zone.
The Czech EU presidency said in a statement that it "welcomes the two-day ceasefire," but "remains however deeply concerned about the situation for the civilians trapped in the conflict zone.
"
The EU presidency "therefore calls for an extension of the pause in order to facilitate humanitarian operations and ensure the physical safety of all civilians," the statement added.
Sri Lankan President Mahinda Rajapakse on Sunday called a two-day truce only to coincide with the traditional New Year on Monday and Tuesday.
The Tamil Tiger rebels said earlier Tuesday that they were ready to negotiate a ceasefire with governme