Matches were suspended on Saturday and Sunday as referees staged a protest after the car of their association president, Leondios Trattos, was damaged in a bomb explosion on Friday.
Nobody was injured but the incident was the latest in a string of attacks against match officials.
"There is no reason for these fixtures not to take place," said referees association secretary Marios Panayi.
"The absention of the referees was for the domestic fixtures. It has absolutely no impact on international games held under FIFA auspices."
Trattos, who has also been targeted in the past, was due to referee the friendly between Ukraine and the United States after the game was moved to the island for security reasons.
However, Ukraine has since cancelled the match due to the current situation in their country.
National football federation president Anatoliy Konkov confirmed: "If we do not have an opportunity to play on home soil, why shall we go to Cyprus in those troubled times for your country?
"We play for our people and country. Our team do not fly to Cyprus and stay at home," Konkov told the ICTV channel.