The Council accepted Russia's proposal that Serbian Prime Minister Vojislav Kostunica be allowed to address the closed session after Ahtisaari and voice Belgrade's opposition to the proposed plan.
A representative of the UN administration in Kosovo (UNMIK) addressed the Council on behalf of Kosovo President Fatmir Sejdiu, who was attending the meeting, but did not address it for protocol reasons.
The United States and the European Union support Ahtisaari's plan for supervised independence as the only viable solution to the Kosovo issue, while veto holder Russia is against it.
A Western diplomat said that Kosovo would be a major topic in the Security Council and that it would be discussed for several weeks.
Russia's UN Ambassador Vitaly Churkin told reporters on Tuesday he was pleased with the accepted procedure of consultations on Kosovo, stressing that it was a good formula.
Churkin was unhappy with the fact that Kosovo representatives were allowed to attend the UN meeting after the United States granted them visas, unlike representatives of Georgia's breakaway province of Abkhazia, who had been repeatedly denied the possibility of addressing the UN because the US refused them visas.
Moscow believes that granting Kosovo independence would set a precedent from the point of view of international law because Kosovo was an autonomous and not a federal unit in the former Yugoslavia.
Speaking to reporters after the start of consultations, Kostunica said the Security Council rejected the plan, which caused confusion among reporters because the Council had only just begun consultations on the matter and a final decision was yet to be made.
"First, I would like to express my satisfaction that the plan on the future status of Kosovo, proposed by special envoy Ahtisaari, was not accepted by the Security Council," the Serbian prime minister said, explaining that his optimism was based on the reservations with which the proposal was met in the Security Council.
Kostunica said that even some EU member states were opposed to the plan and that it did not receive an applause in the Security Council as had been expected. When asked by reporters to specify which permanent Security Council members were opposed to the plan, he avoided an answer.
Kostunica said that Serbia supported Russia's plan for new negotiations with a new mediator.
Sejdiu told reporters that Kosovo Albanians wanted to conclude the process based on Ahtisaari's proposal as soon as possible.
"It is extremely important to build a modern state based on democratic values and respect the rights of all its citizens. Kosovo should take its part of responsibility for stability in the region and for development," Sejdiu said, adding that "any delay of that process would be counterproductive."
France's UN Ambassador Jean-Marc de La Sabliere said that any delay of a solution to the Kosovo issue was risky and that the UN Security Council should decide on the future of Kosovo in the coming weeks.
"What is at stake is the stability of Europe and this is the completion of the process of the break-up of the former Yugoslavia, so it's a very specific situation," the French diplomat said, adding that keeping the status quo was not an option and that it might be even more dangerous.
The Security Council president, British Ambassador Emyr Joens Parry, said that there was "considerable support" within the Council for supervised independence for Kosovo, but that a vote on a resolution on Kosovo should not be expected soon.
Parry told reporters that the governments of Great Britain, France, Germany, Italy, the United States and Russia were likely to start drafting a resolution on Kosovo this month, and that the Council would decide in the coming days on whether its representatives would visit Kosovo.
"I will expect further (council) discussions this month. I don't think it's likely there will be an early presentation of a Security Council resolution though," he said, as quoted by Reuters news agency.