Vojislav Kostunica said the new constitution, approved unanimously by parliament on Saturday, would ensure that "Serbia will defend Kosovo with all democratic and legal means".
"Kosovo is ours," he told parliament on Saturday.
Kostunica set no date for the election, but said it would probably be in December.
Parliament set an October 28-29 date for the referendum on the constitution.
If the constitution is ratified by the public vote, Serbia can call for new elections 45 days later.
The new constitution has been drawn up as Nato pushes ahead with a plan to hold a referendum in Kosovo on independence from Serbia.
The proposed referendum in Kosovo would almost certainly see the majority Albanian Muslim province vote to separate from the mainly Christian Orthodox Serbian state.
The adoption of a new constitution by Serbs in a referendum would signal strong public opposition to giving up Kosovo, a region which has always been regarded as part of ''Old Serbia'' by Serbs.
President Tadic has praised the new constitution
"The province of Kosovo is an integral part of Serbian territory, it has a position of substantial autonomy within the framework of the sovereign state of Serbia," the new constitution read.
"From such a position is derived the constitutional obligation of all state institutions to protect the interest of Serbia in Kosovo in all internal and foreign political relations."
Boris Tadic, the Serbian president, said the new constitution would define Serbia as a "modern, European state".
Serbia's present constitution has been rendered largely obsolete by the departure of Montenegro from the Yugoslav federation after its formal declaration of independence in June.
Kostunica's initiative comes despite continuing talks over the future status of the UN-run province between Serbian officials and the ethnic Albanian leadership in Kosovo, who are demanding independence.
"I see no reason to wait for Kosovo's status to be solved first," Kostunica told a press conference earlier in the day.
"For Serbia, the issue of Kosovo is solved by the fact that it is an integral part of Serbia and that international law confirms this."
Several hundred demonstrators chanted slogans against the constitution outside parliament on Saturday, saying it was a rushed job pushed through for political rather than constitutional reasons.
Armed Kosovan separatists fought the Serbian army in 1998-99, until Nato bombed Serbia for nearly three months to compel its withdrawal from the territory.