Cavusoglu's remarks came during a press conference in Lefkosa, the capital of the Turkish Republic of Northern Cyprus (TRNC), alongside TRNC Prime Minister Huseyin Ozgurgun.
"Turkey will support Cyprus peace talks as it always has," Cavusoglu said, adding that Turkey is closely following developments on the Cyprus issue.
Reunification talks between the Greek and Turkish communities on the island resumed in May 2015 and are expected to be resolved by the end of this year with the formation of a federal administration.
Previous negotiations stalled in October 2014 due to a dispute over gas exploration.
The eastern Mediterranean island was divided into a Turkish Cypriot state in the north and a Greek Cypriot administration in the south after a 1974 military coup was followed by the intervention of Turkey as a guarantor power.
For his part, Prime Minister Ozgurgun said that Turkey and Northern Cyprus are two states but one nation.
Referring to the July 15 defeated coup in Turkey, blamed by Turkish officials on the Fetullah Terrorist Organization (FETO), Ozgurgun said the TRNC recognizes the group as a terrorist organization.
"Northern Cyprus will not tolerate any negative development in our ‘homeland’ Turkey,” he said, adding, “Because we know that a powerful Turkey means a powerful Northern Cyprus."
News conference with President Akinci
After Ozgurgun, Cavusoglu met Mustafa Akinci, the president of the TRNC.
"We will continue to give support to a solution that would be accepted by both parts [of the island]," Cavusoglu told reporters alongside Akinci.
Cavusoglu said the aim is to ensure a "permanent" peace and solution, adding: "We are ready to make any kind of contribution, including trust-building steps and measures."
Akinci said they set this year as the target year for a solution. "This is the aim for us all. Turkey supports this aim all the way," he added.
He said: "We strive for a solution that both sides can accept."