Rosemary DiCarlo, a US envoy, said that the Serbian request was "unnecessary and unhelpful", and that "Kosovo's independence is irreversible".
John Sawyers, Britain's UN ambassador, reiterated London's full support for the ICJ but said that this did not mean it backed Belgrade's resolution, which is why Britain abstained.
"The reason is that the Serbian request is primarily for political rather than legal reasons," he said.
"It is designed to slow down Kosovo's emergence as a widely recognised independent nation, playing its part in the international
institutions of the world."
Vuk Jeremic, the Serbian foreign minister, rejected the suggestion that its move was politically motivated and said seeking ICJ advice would "reduce tensions in the region".
"Sending this question to the ICJ would prevent the Kosovo crisis from serving as a deeply problematic precedent in any part of the global where secessionist ambitions are harboured," he said.
Although the Serbian resolution was approved by the General Assembly, most of the 27 European Union member states abstained from the vote. The US, like Albania, opposed it.
The divisions in the EU, however, were clear. Cyprus, Slovakia, Romania, Greece and Spain were among those who broke ranks with the majority of EU members and supported Serbia.