"EULEX represents an important, I would say even a capital, step in a difficult, chaotic situation," French foreign minister Bernard Kouchner, whose country currently holds the six-month rotating EU presidency, told journalists on Monday, announcing the deployment.
EU foreign affairs chief Javier Solana added: "We are co-operating very constructively with the Serbian government and also with Pristina. So, I hope very much that we will turn a page tomorrow [Tuesday] in the development of EULEX."
The EU's Kosovo mission is the largest deployment ever mounted by the bloc. It will be composed of some 2,000 individuals, starting with 1,400 international and 500 local people from today, reaching some 1,900 international and 1,100 national members by spring 2009.
The mission was established on 4 February this year as "a technical mission that will mentor, monitor and advise [in the rule of law area - specifically in the police, judiciary and customs areas] whilst retaining a number of limited executive powers."
EULEX has already faced problems and delays, as Serbs and Kosovars failed to agree on what its mandate should be and where it should operate.
Following Serb protests, UN Secretary General Ban Ki-moon last month proposed a six-point compromise plan that would clear the way for the mission to begin, but that also weakened the EULEX mandate, and stressed the mission would remain "neutral" as regards Kosovo's status.
This in turn provoked protests among Kosovars, who felt this went against their country's sovereignty - after nine years of UN governance, Kosovo proclaimed unilateral independence from Serbia in February, a move Belgrade never recognised.
Both sides agreed to co-operate fully with EULEX in November, but still disagree on some points, and Pristina still categorically opposes the elements of the plan that are neutral to its status.
EU calls on Croatia to speed up reforms
Separately, the 27 EU foreign ministers meeting in Brussels on Monday also assessed the progress towards the EU of the western Balkan countries and Turkey.
In particular, they called on Croatia to make additional efforts in judicial, administrative and economic reform, the fight against corruption and organised crime, the protection of minorities, the return of refugees, and the prosecution of war crimes.
However, Zagreb's long-running border dispute with its neighbour and EU member Slovenia is one of the crucial elements that "make things drag a little" as far as Croatia's EU accession is concerned, one diplomat said.
In October, Slovenia blocked Croatia's accession talks over a 17-year-old row about their common sea and land borders, as it had concerns that documentation offered by Croatia in the talks could be prejudicial to the outcome of the dispute.
"Slovenia supports Croatia's EU membership as long as it doesn't harm our national interest," Slovenian Prime Minister Borut Pahor told journalists in Brussels last week.
"If we can find [a] solution, then probably Slovenia will have no reservations on supporting further negotiations between Croatia and the EU," he added.
On Monday, Mr Kouchner said he had been "surprised" by the level the problem had reached.
"We must take the time to talk to our friends ...to calm down," and solve this issue, he added.
The EU is hoping for a breakthrough by 19 December, when it had planned to open new chapters of both Croatia's and Turkey's accession packages.