The monument glorifies the assassinators of Ottoman and Azerbaijani officials in the early 1920s.
Speaking to broadcaster NTV, Çavuşoğlu said Türkiye would take further steps if the monument is not removed.
Previously, low-cost Armenian airline FlyOne Armenia said the country closed its airspace to their planes on Saturday, "without warning."
"For reasons incomprehensible to us and with no visible grounds, Turkish aviation authorities canceled the permission previously granted to the FlyOne Armenia airline to operate flights to Europe through Turkish airspace," the domestic Armenpress news agency cited the carrier's board chairperson as saying.
Ankara earlier condemned the inauguration of the monument.
"We strongly condemn the opening of the 'Nemesis Monument' in Yerevan, which is dedicated to the perpetrators of the assassinations against Ottoman political and military leaders in the early 1920s, and Azerbaijani officials of the time, as well as even some Ottoman citizens of Armenian origin," the Foreign Ministry said in a statement.
"The opening of this shameful monument glorifies a bloody act of terror that led to heinous terrorist attacks in which 31 of our diplomats and their family members were murdered," it said.
The statement also underlined that the way these events were portrayed by Armenian media indicated that a distorted and unacceptable understanding of history persisted among some people.
"Such provocative steps, which are incompatible with the spirit of the normalization process between Türkiye and Armenia, will in no way contribute to the efforts to establish lasting and sustainable peace and stability in the region, on the contrary, they will negatively affect the normalization process," it said.
According to data compiled by Anadolu Agency (AA), a total of 77 people – 58 of them Turkish citizens, including 31 diplomats and members of their families – were killed in attacks from 1973 to 1986 carried out by terrorist groups, including the Armenian Secret Army for the Liberation of Armenia (ASALA), Justice Commandos of the "Armenian Genocide" (JCAG) and the Armenian Revolutionary Army (ARA).
The deadly campaign began in 1973 with the assassination of Türkiye's Consul General in Los Angeles Mehmet Baydar and diplomat Bahadır Demir by a terrorist named Gourgen Yanikian. ASALA was the first Armenian terrorist group to attack Türkiye and it not only targeted Türkiye, but also other countries.
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