Turkish Cypriot President Rauf Denktash has appointed the leader of a pro-European party to form the next government.
Talat wants a reunified island to join the EU
Mehmet Ali Talat has until February to present a cabinet to avoid new polls.
His Republican Turkish Party and their allies supporting a UN plan to unite the island control 25 seats in 50-seat breakaway parliament.
Mr Denktash has said fresh elections will be held if no party manages a working parliamentary majority.
The president - whose position remains unchanged by the hung parliament - has opposed re-unifying the island that has been divided since 1974.
Cyprus is due to join the European Union on 1 May.
EU law will not apply to the north of the country if an agreement to re-unite the island has not been reached by then.
"The president has appointed me to form a government that can get a vote of confidence from the parliament," Mr Talat said after meeting President Denktash.
"The Turkish Cypriot people need, in the shortest possible delay, a government that can win the confidence of the [Turkish Cypriot] parliament," he said.
"The date of 1 May is our main objective," Mr Talat said.
Mr Denktash says the UN plan will lead to southern domination
The Turkish Cypriot opposition won 48% of the vote in the 14 December poll, just two points ahead of the governing nationalists.
Mr Denktash said the poll showed voters backed reunification and European Union membership, but not at any price.
Mr Denktash has also called on the two main parties to form a grand coalition with one another.
Opposition leaders had said they would replace him as the Turkish Cypriot negotiator in reunification talks.
Mr Denktash and his supporters have argued that the UN-backed plan would lead to the domination of the north by the south.
THE NEW PARLIAMENT
Republican Turkish Party
National Unity Party (nationalist) - 18
Democrat Party (nationalist) - 7
Peace and Democracy Movement (pro-EU) - 6
Correspondents have said the outcome of the election makes it highly unlikely that Cyprus will be re-united by May, meaning in effect that only southern Cyprus will join the EU.
The European Union has urged both Turkish and Greek Cypriots to resume the stalled peace talks quickly.
Cyprus has been partitioned since 1974, when a short-lived Greek-inspired coup prompted a Turkish invasion of the northern third of the island.
Thousands of people were displaced from their homes and many have never returned. The Turkish Republic of Northern Cyprus was declared in 1983, but has been recognised only by Turkey itself.