"Without justice there can be no reconciliation in Yugoslavia and without reconciliation there can be no peace," Mr Fischer said. "But Milosevic is not our first priority."
EU foreign ministers agreed to lift their oil embargo and a ban on commercial flights.
But other measures targeted specifically against the former president, Slobodan Milosevic, and his associates, will stay in place.
The EU's wide-ranging sanctions were imposed in 1998 as part of an international effort to stop Serb-sponsored abuses of ethnic Albanians in Kosovo.
Democracy
At their meeting in Luxembourg foreign ministers were unanimous in their decision.
"We promised that we would change our policy once democracy had won. That happened on Saturday," the German Foreign Minister Joschka Fischer told reporters.
The foreign ministers appear to have quietly dropped demands that aid be conditional on Mr Milosevic being handed over to the International War Crimes Tribunal at The Hague.
"Without justice there can be no reconciliation in Yugoslavia and without reconciliation there can be no peace," Mr Fischer said. "But Milosevic is not our first priority."
The French Foreign Minister, Hubert Vedrine, is due to meet Mr Kostunica in Belgrade on Tuesday to discuss the sanctions issue.
Apart from the sanctions, the EU ministers have been preparing a series of aid packages to assist with the rebuilding of Yugoslavia's war-shattered infrastructure.
Details of the packages are likely to be revealed at an EU summit in Biarritz at the end of the week, to which Mr Kostunica has been invited.
An international arms embargo against Yugoslavia remains in place as it was imposed not by the EU but by the United Nations.
Double resignation
In Yugoslavia itself the federal Prime Minister, Momir Bulatovic - a key Milosevic ally - has resigned after talks with Mr Kostunica.
And in a further blow to Mr Milosevic the powerful Serbian Interior Minister Vlajko Stojiljkovic - an indicted war criminal - has resigned at a session of the Serbian parliament.
The BBC Belgrade correspondent, Jacky Rowland, says opposition parties had been pushing for the resignation of Mr Stojiljkovic after the popular uprising last week against Mr Milosevic.
They did not want one of his key allies in charge of the Serbian police force.
In addition, the Serbian parliament, a power base for the supporters of Mr Milosevic, is to be dissolved with fresh elections on 19 December.
There has been no new word on the whereabouts of the ousted president himself, following his television address in Belgrade on Friday.
But on Monday Mr Milosevic's son Marko was turned back as he attempted to enter China, which had been seen as a possible bolthole for the family.