"Of course we have different views but we need to continue to talk in order to narrow our differences," Cavusoglu was quoted as saying by the state-run Anatolia news agency.
Erdogan and Putin: ex-pals turned sworn foes who won't back down
Cavusoglu was speaking at a breakfast given for Russian citizens living in his hometown of Antalya, a popular tourist destination for Russian tourists on Turkey's Mediterranean coast.
The downing of the Russian warplane on the Turkish-Syria border on November 24 has strained ties between Ankara and Moscow which have traded accusations in recent days.
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Cavusoglu met with his Russian counterpart Sergei Lavrov in Belgrade on Thursday in the first high-level contact between the two sides since the disputed plane incident..
"I had a very useful meeting with my friend Sergei Lavrov," Cavusoglu said on Saturday. "We discussed all issues in a positive atmosphere."
The foreign minister warned against "inaccurate" statements or news disseminating in Russia.
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"One day problems will be resolved but the seeds of discord you had sown among people could continue for a long time. Therefore, everyone should act responsibly," Cavusoglu said.
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