Papadopoulos said he was ready to be accommodating
United Nations Secretary General Kofi Annan has held talks with Cypriot leaders, with only days left to find agreement on a plan to unite the divided island.
Mr Annan said he expected progress towards a deal, after hour-long negotiations with Greek Cypriot President-elect Tassos Papadopoulos and Turkish Cypriot leader Rauf Denktash.
Mr Papadopoulos said after the meeting he was "ready to be accommodating" but that the Turkish side should be too.
The UN has set Friday as the deadline for a settlement, and although there are signs this could be extended by up to a week, most of the main players appear pessimistic about a deal.
Mr Annan flew in from Greece earlier aboard a white UN jet, telling Greek and Turkish Cypriots they had a "rendezvous with destiny".
A newly-revised version of the UN plan has already earned criticism from both sides - although Mr Annan insists it is the final draft.
Let the word go out to Greek Cypriots and Turkish Cypriots alike that you have a rendezvous with destiny
UN Secretary General
Mr Denktash said the revisions gave the Greek Cypriots cake and the Turkish Cypriots peanuts.
On the Greek Cypriot side, Cyprus Foreign Minister Yiannakis Kassoulides said: "Accepting the revised plan demands very painful
concessions on our part."
The Greek Government has already said the chances of a settlement this week are virtually non-existent.
But after arriving at Larnaca airport, Mr Annan continued to press the divided communities to find peace.
"Let the word go out to Greek Cypriots and Turkish Cypriots alike that you have a rendezvous with destiny," Mr Annan said.
"When I came here in mid-May, I looked into the people's eyes and I saw that they wanted to bring an end to the longstanding dispute that has torn this beautiful island apart for decades."
Mr Annan has already warned Greek and Turkish Cypriot leaders that time is running out to end the bitter 29-year separation.
He wants the two sides to settle now so that Cyprus can join the European Union as a united country.
AFP news agency quoted UN spokesman Brian Kelly as saying that the three men, along with outgoing Greek Cypriot President Glafcos Clerides, will meet at 1000 local time (0800 GMT) on Thursday in the buffer zone between the two halves.
A treaty admitting Cyprus to the EU is due to be signed in April, and failure to reunite the island before that would mean EU membership applying, in effect, only to the Greek-run part.
Any deal would have to be put to a referendum of all islanders on 30 March.
The sticking points include how much land the Turkish Cypriots must cede, and the right of return for Greek Cypriot refugees.
Greek Cypriots are concerned by a clause that would only allow a reported 20,000 refugees to return to land occupied by Turkish troops when the island was divided in 1974.
But Rauf Denktash says the changes would mean 40,000 people on his side of the buffer zone being displaced from their homes.
Cyprus has been divided since 1974, when Turkish troops invaded in response to a short-lived Greek coup.