Foreign Minister Mevlut Cavusoglu announced earlier that talks to reunify the island of Cyprus ended in failure in Crans-Montana.
Representatives from the EU, the Turkish and Greek Cypriot leaderships, and the guarantor nations of Turkey, Greece and the U.K., had participated in the intense discussions that began at the end of last month to resolve the dispute.
The UN is seeking a peace deal to unite Cyprus under a federal umbrella that could also define the future of Europe's relations with Turkey, a key player in the conflict.
The Eastern Mediterranean island has been divided since 1974, when a Greek Cypriot coup was followed by violence against the island's Turks, and Ankara's intervention as a guarantor power.
Speaking to reporters in Ankara on Friday, Yildirim said Turkey would continue its positive attitude towards finding a permanent solution to the dispute.
“Either through United Nations or other organizations, if they want a permanent, fair and equal solution on the island, we will always continue to be constructive,” he said.
"Turkey will use international law to protect the rights of Turkish Republic of Northern Cyprus and our brothers living there.”
He said Turkey had made every effort to resolve the issue since the beginning of the talks and proved its sincerity towards peace.
"Turkey showed clearly to the United Nations, the European Union and other guarantor countries that it is the side that is seeking a solution sincerely," he said.
“However, after the referendum in 2004, Southern Cyprus's unilateral full membership to the European Union actually paved the way towards the present situation.
"The Greek Cypriot side did not show the expected constructive attitude towards the solution, unfortunately, with the ease of being a member of the European Union.”
About the protest march of opposition People’s Republican Party (CHP) from the capital Ankara to Istanbul, Yildirim said the march would end with an open-air meeting on Saturday.
"I hope they will complete this march in peace without rampage or malicious intrusion,” he said.
He reiterated that parliament is the place to seek for solutions to problems. “Let’s strive to provide justice, to work better and to come on time; however, not by coming out on roads or by marches.”
CHP leader Kemal Kilicdaroglu began a 350-kilometer (217-mile) trek on June 15 following the jailing of their party lawmaker Enis Berberoglu who was sentenced to 25 years in prison for giving information to a newspaper on the alleged transportation of Turkish arms to Syria.