With Greece and Turkey involved in delicate negotiations over the future of Cyprus, and with Athens a key supporter of Turkey's European Union ambitions, many Turks hope the new government will continue with the old policies.
It seems they are unlikely to be disappointed.
"One of the most amazing things about the election," John Psaropoulos, editor of the weekly Athens News, told Aljazeera.net, "is that for the first time in history, we have had a change of government without it meaning a change of foreign policy."
Since 1999, when disastrous earthquakes struck both Turkey and Greece, the two Aegean neighbours have been following a policy of rapprochement – trying to end decades of hostility.
Bad relations had followed historical animosities and a number of major disputes. Cyprus, effectively divided after an Athens-backed coup in 1974 and a subsequent Turkish invasion, has long been a central cause of disagreement.
The division of Cyprus is an old
conflict for Greece and Turkey
Now, Greece and Turkey are key players in the latest UN-sponsored attempt to reunite the island. Turkish and Greek Cypriot leaders are currently meeting in Nicosia to negotiate on this issue.
Meanwhile, the two countries have disputes over maritime and air space in the Aegean, as well as conflicting claims to ownership over dozens of tiny islands located off the Turkish coast – but which Athens claims are within Greek territory.
Talk of war
The two neighbours nearly came to war over one such island, known as Kardak to the Turks and Imia to the Greeks, back in 1996.
However, in 1999, talk of war changed. Athens adopted a new policy that promoted warmer relations with Turkey.
It was the brainchild of George Papandreou, the man who lost the general elections. He was foreign minister in the centre-left PASOK government that ruled Greece before last Sunday, and which had made him prime minister last month.
"Greece stepped back," said Psaropoulos. "Under Papandreou's leadership, Athens said it no longer had any objections to Turkey joining the EU. That changed everything."
It was the beginning of a very successful new foreign policy – with Ankara responding positively. Turkey has long wanted to join the EU while Greece has been a member since the early 1980s.
Athens' policy shift
In the past, Athens had long objected to its neighbour being allowed in, citing Turkey's Muslim culture, history and slower economic progress as objections.
Papandreou managed to shift all that around and make Greece one of Turkey’s strongest EU membership advocates.
Turkey wants to join the EU, an
effort that Greece supports
"The Greek government managed to tie all its disputes with Turkey to the issue of Turkey joining the EU," Hasan Onal, assistant professor of international relations at Ankara’s Bilkent University, told Aljazeera.net.
"The Turkish government has been prepared to go along with this too, on the strength of a rather iffy promise of eventual EU membership."
"The shift meant using the EU to gain leverage in solving the Cyprus and Aegean issues," added Psaropoulos. "It has been such an effective foreign policy move; no one would want to change it."
New Democracy party
"We will all together, united, give the great battle to safeguard a just, functional and European solution to the political problem of Cyprus," Karamanlis said on election day.
But Karamanlis's New Democracy (ND) party made little play of foreign policy issues in the election campaign, and Karamanlis had in fact visited Ankara last year to tell the Turkish parliament that he did not intend to make any change in policy direction.
As a result, the election campaign was fought on domestic rather than international issues, itself a major difference from previous years.
"The present Turkish government appears to be giving too much away in its efforts to get a deal on joining the European Union"
assistant professor of international relations,
"There were two issues the parties decided not to fight over: The Olympics and Cyprus," said Psaropoulos. "In fact, from Cyprus, this truce widened out to a decision by both not to make foreign policy an issue at all."
But the past was still a cause for reserving judgment.
The last time the centre-right ND were in office for any length of time – back in the 1980s - relations between Greece and Turkey were at a frightening low.
"The 1970s and 1980s were a very difficult time," recalled Psaropoulos. "It was something of a cold war period."
Now all that has changed, with few expecting any return to those darker days.
Onal, himself a sceptic, said: "I am not sure if it is possible to say that what has been happening in recent years is really an improvement."
"The present Turkish government appears to be giving too much away in its efforts to get a deal on joining the European Union. This is quite a dangerous business, as I am not sure how far the Turkish public will go along with any apparent sellout on issues such as Cyprus or the Aegean."
Meanwhile, many Turks are also concerned about the status of the ethnic Turkish minority in northern Greece.
"These people had been subjected to official discrimination for a long time," said Psaropoulos. "They were denied equal treatment in the army and civil service. For a long time, it was even taboo to refer to them as Turks – the official description is 'Muslim Greeks'."
"The lack of any real dispute over foreign policy is in itself a major change in Greek politics. It is perhaps the beginning of a new chapter"
editor of the weekly Athens News
Papandreou had also tried to change all that, apologising to the Turkish minority for past discrimination during his election campaign.
However, Karamanlis's ND stayed clear of this issue.
"It is early days," said Onal. "Yet, I suspect no new government in Athens is going to want to change much in a process that is very much in its favour."
"The lack of any real dispute over foreign policy is in itself a major change in Greek politics," added Psaropoulos. "It is perhaps the beginning of a new chapter."