Yildirim was speaking in the TRNC where he attended ceremonies marking the 43rd anniversary of Turkey’s 1974 intervention into the Cyprus conflict as a guarantor power.
Recent UN-backed reunification talks between Greek and Turkish Cypriots, plus Ankara, London and Athens, recently broke down in Switzerland amid recriminations.
Addressing a commemoration, Yildirim said: "It is a serious contradiction and injustice that Turkish Cypriots have paid for the uncompromising approach of the Greek side for years.”
"The rights and prosperity of Turkish Cypriots are a national matter for us."
Yildirim also said "unfair steps" taken by the Greek Cypriot side had encouraged deadlock in the talks.
"It was clearly understood that the Greek Cypriots were not ready for a solution," he added.
TRNC President Mustafa Akinci, Prime Minister Huseyin Ozgurgun, and Parliament Speaker Sibel Siber, as well as Turkish Foreign Minister Mevlut Cavusoglu also attended the ceremony at the Ataturk Memorial in Lefkosa.
President Akinci, writing in an official memorial book, also said Turkish Cypriots "had no responsibility" for the failure of the Switzerland talks.
The eastern Mediterranean island has been divided since 1974 when Turkish soldiers interceded under Ankara’s guarantor status to protect the Turkish community from unrest.
Violence broke out amid a Greek Cypriot attempt to forcibly unite Cyprus with Greece then ruled by a right-wing military junta. Turkey sent 40,000 troops -- Operation Atilla -- to the island’s north.
As a result of Greek Cypriot attacks, at least 30,000 Turkish Cypriots were displaced from their villages and the Turkish Cypriot population was forced to seek refuge.
Yildirim said the 1974 operation was "a turning point in the island's history," and that Turkey showed the world it would not allow ‘enosis’ -- a Greek takeover of Cyprus.
He also recalled how negotiations over Cyprus resumed after a failed 2004 deal put forward by former U.N. Secretary General Kofi Annan to reunify the Turkish Cypriot and Greek Cypriot communities.
The plan was rejected in a referendum by the Greek portion of the island whereas Turkish Cypriots voted in favor of the Annan plan.
Yildirim said Turkish Cypriots had "passed the exam" by voting Yes in the referendum. The Greek Cypriot side's No approach to living together "continues today," he added.