Cyprus has been divided since 1974 when Turkey invaded in response to a coup
by supporters of reunification with Greece.
The basis of the talks had been reuniting the island as a bizonal federation, though the UBP said it wanted a rethink of the process.
Talat has held talks with Dimitris Christofias, the Greek Cypriot president, which many have viewed as the most realistic attempts at a lasting peace in decades.
Talat's Republican Turkish Party had 25 deputies in the last assembly, while the UBP had only 16.
But Sunday's vote is expected to change the ratio, one year before Talat's term as president expires in April 2010, giving him less room for manoeuvres in unity talks.
Talat said that regardless of who wins, the winner of the elections should not disrupt current peace negotiations.
"A government in [Northern Cyrpus] that seeks to scupper the talks will also be harming Turkey's EU accession process," he told Havadis, a Turkish Cypriot daily.
The UBP, led by Dervis Eroglu, had a 15 point lead over Talat's party. Eroglu said that a unified Cyprus should not be the only option and promised to appoint a representative to accompany Talat in negotiations with Christofias.
"Everything will be easier if it is universally accepted that we are a nation and that we have a state," Eroglu said.
}Greek Cypriots represent Cyprus in the European Union, and say they will not allow Turkey to join the bloc as long as the island remains divided.