A couple of things here. Firstly, Greece did push actively for Cyprus's EU accession. But the EU was not reluctant to accept Cyprus. It was actually very keen because it saw Cyprus as an excellent candidate and also saw Cyprus' EU accession as a symbol of its own values and sovereignty.
Some background. While it's true that Greek gov't representatives, particularly Foreign Ministry Secretary-General Yannis Kranidiotis, prior to his death in 1998, periodically uttered threats that Greece was prepared to veto any Enlargement of the EU that did not include Cyprus, Cyprus was already regarded by the EU as an excellent candidate on its own terms with a well functioning democracy and a flourishing economy.
The majority view of EU countries was that Cyprus was the best candidate for accession and this should not be dependant on a solution. This was because Cyprus was not seen as responsible for the island's division. Turkey was not only seen as the main cause of the problem. It was also regarded as the major obstacle to a solution. As one German MEP put it:
The reunification of Cyprus must not be a precondition for accession… for Cyprus must not become a hostage to Turkey and Turkey must not be granted any right of veto on this question. Cyprus must not be penalized twice over.Cyprus's accession also became a question of the EU defending its values and sovereignty.
While some speakers saw this as a matter of justice for the RoC, others deemed it a question of principle concerning the sovereignty of the EU itself. For instance, it was declared completely unacceptable for a non-EU member – and ‘a foreign occupant’ to boot – ‘to dictate the date and pace of accession negotiations’ between the Union and its applicants. On another occasion, a Greek MEP declared that proceeding with the accession process constituted ‘a message to all quarters’ that the European Union would ‘proceed on the basis of its own principles and perceptions … without allowing anyone to dictate how issues relating to human rights, democracy, international standing and international law are to be handled’.In conclusion:
Greek arguments in favour of allowing the accession process of the RoC to move ahead fell on willing ears. This was because they resonated with values held to be central to the EU identity. In our EP case study, it was apparent that Greek MEPs played an active role in debates on Cyprus. But their views were very much part of the parliamentary mainstream. The essential point was that excluding the RoC on the grounds of the unresolved conflict would have been a morally untenable position in the context of the value-based perceptions of EU Enlargement analysed above. In this respect, the admission of the RoC may be seen not as something which happened by accident, the result of an incremental slide towards Cypriot accession, but as a decision taken by a community of values in order to preserve its own identity.See this
article for all quotes and background.