Speaking at a joint press conference after meeting Montenegrin President Filip Vujanovic, Tadic said Montenegro-Serbia relations should be defined in line with the new state of affairs as soon as possible.
Vujanovic said he and Tadic assessed that the competence of the Supreme Defence Council of the state union of Serbia and Montenegro should be transferred to Montenegro and Serbia immediately after the formal proclamation of Montenegro's independence.
The two presidents underlined that there existed common interests in defence and diplomacy, but did not mention models of possible cooperation in the two areas.
Tadic said he and his Montenegrin counterpart did not discuss Podgorica's previous proposal to form an alliance of independent states, but did underline that the condition for such a model would be the recognition of sovereign Montenegro and sovereign Serbia.
At a press conference immediately after last week's referendum, Montenegrin Prime Minister Milo Djukanovic said such a proposal "is no longer on the table".
Tadic today arrived on a first official visit to Podgorica after over 55 per cent of Montenegrins voted for independence last Sunday.
Later today he is scheduled to meet other Montenegrin leaders as well as Predrag Bulatovic, the head of the unionist bloc, which advocated Montenegro's remaining in the state union with Serbia.