"We will not be the cause of any tension; we will work with tolerance and understanding. We hope that other parties will have the same approach," she said.
"This is an important opportunity to solve the Kurdish issue."
But in a gesture likely to anger the authorities, party members in the southeastern city of Diyarbakir celebrated the election results by shouting slogans in support of the jailed Kurdish rebel chief, Abdullah Ocalan, according to the Dogan news agency.
Several Kurdish legislators were ousted from parliament in 1994 for having ties to Kurdish rebels, and one of them, Leyla Zana, urged Turkey last week to accept a federal structure and declare the Kurdish-majority southeast as "Kurdistan".
Prosecutor Mustafa Kucuk on Saturday filed charges of separatism against Zana for her remarks.
Zana, who served more than a decade in prison for having ties to rebels, had campaigned for the party but was not allowed to run for parliament again herself because of her criminal record.
Tugluk praised Zana for her work to advance Kurdish rights, but distanced the party from her remarks.
"We don't have a federal system on our agenda," she said.
Tugluk also faces prosecution on separatism charges for praising Ocalan and using an honorific title for him.
Turkey has been fighting rebels of the Kurdistan Workers' Party (PKK) since 1984 in a war that has killed tens of thousands of people.
Abdullah Gul, the foreign minister and the prime minister's previous controversial nominee for president, ruled out co-operation with Kurdish legislators in parliament, as have almost all parties that campaigned for Sunday's elections, unless Kurdish legislators denounce the PKK as a terrorist organisation.
Turkey has threatened to enter Iraq to
attack Kurdish rebel bases [AFP]
Pro-Kurdish politicians have refrained from doing so.
Meanwhile, a Kurdish rebel commander said on Sunday in neighbouring Iraq that he believed the Turkish military would launch an offensive against separatist bases in northern Iraq.
Murat Karayilan said his fighters were prepared for battle.
Turkey has threatened to stage such an incursion if talks with Iraq and the US fail to produce effective measures against the rebels.