The former Finnish president told Draskovic and Kostunica that he would comply with recommendations of the UN Secretary General and basic principles of the Kosovo Contact Group in his efforts to help solve the status of Kosovo.
He stressed that a final decision on the UN-administrated province would be made by the UN Security Council.
According to a press release issued by Serbia-Montenegro's Foreign Ministry, Draskovic told Ahtisaari that "international recognition of Kosovo would produce a domino effect sending shockwaves through the Balkans and all over Europe and the world".
"For Serbia-Montenegro, namely for the Republic of Serbia, it is of key importance to see that the current status of the internationally recognised borders of Serbia-Montenegro with Albania and Macedonia remains unchanged," Draskovic said.
Kostunica presented Ahtisaari with the Kosovo resolution which the Serbian parliament adopted recently.
Kostunica also suggested that during his next tour of the region as part of his shuttle diplomacy the UN envoy should also visit neighbouring countries, Romania, Bulgaria and Croatia and hold talks with those countries' officials who, he said, expressed their principled positions on the issue of Kosovo's future status.
On Friday Ahtisaari will meet the head of the Serbian Orthodox Church, Patriarch Pavle, Serbia's President Boris Tadic, and foreign diplomats in the Serbian capital, and will hold a news conference at the end of his visit.
After Belgrade he will tour the Montenegrin capital of Podgorica, Macedonia's Skopje and Albania's Tirana.
On late Wednesday night, Serbian President Tadic sent the Serbian government a document with basic guidelines for negotiations, which he had recently discussed with Russia's President Vladimir Putin. The proposal provides for the establishment of two entities in Kosovo, one being predominantly populated by Albanians and the other by Serbs.
Serbia's government on Thursday announced the composition of its negotiating team, to be led by Kostunica, Tadic and Draskovic.