It is unclear how the two protesters were killed and who injured them. Around 70 people received hospital treatment following the clashes.
"It is totally regrettable that two lives were lost as a result of wanton breach of security at the government buildings," Stephen Curtis, the UN police commissioner, said on Sunday.
"The demonstrators at the government buildings compelled the police to take defensive measures to restore order. Any death is disheartening and saddens us greatly."
Following the violence Kosovo's top leaders gathered for an emergency meeting and the province's prime minister, Agim Ceku, canceled a planned visit to China.
UN plans disputed
Martti Ahtisaari, chief UN envoy, unveiled his proposal for Kosovo's future status a week ago.
The plan does not explicitly call for Kosovo's independence from Serbia, but spells out conditions for self-rule - including a flag, anthem, army and constitution, and the right to apply for membership in international organisations.
Kosovo's Serb minority would have a high degree of control over their own affairs.
However ethnic Albanian opponents of the plan say the self-rule envisioned for Kosovo's Serb minority could lead to the creation of a separate Serb entity within Kosovo.
Activists also rejected parts of the plan that call for the establishment of a new international mission that would have powers to annul decisions or laws that run against the plan itself.
The plan, which needs approval from UN Security Council to come into force, was endorsed by Kosovo's ethnic Albanian leaders but rejected by Serbian officials in Belgrade who refuse to give up the province, considered Serbia's historic heartland.