However, the two leaders continue to disagree about the two European bailouts that have kept the country's finances afloat, more or less, in recent years. Samaras and New Democracy are pro-bailout, while Tsipras and Syriza are anti-bailout.
In the elections for the 300-seat unicameral Hellenic Parliament, official results showed New Democracy won 29.7 percent of the vote and 129 seats, and Syriza won 26.9 percent of the vote and 71 seats, according to the Associated Press.
It is anticipated Samaras will attempt to form a majority coalition with the center-left Pasok party, which also is pro-bailout and took third place in the elections on Sunday, with 12.5 percent of the vote and 33 seats, the AP reported. It is expected this attempt will be successful.
However, the closeness of the elections indicates Greece continues to be deeply divided about the whole bailout experience, which in turn suggests Syriza -- and the angry sentiment it represents -- is no flash in the pan.
Calling for a national salvation government, Samaras said Greeks had cast their ballots to stay in the euro zone and that he wanted to form a coalition government as soon as possible, BBC News reported.
There will be no more adventures, Samaras said. Greece's place in Europe will not be put in doubt.
However, the coalition negotiations could be difficult, BBC News said.
Evangelos Venizelos, the leader of Pasok, proposed a broad four-party coalition consisting of New Democracy, Syriza and his own organization, as well as the Democratic Left party, which appears to have won 6.1 percent of the vote and 18 seats. No decision can be taken without this national unity, Venizelos said.
Given Tsipras' intransigent opposition to Greece's bailouts -- and, more to the point, the onerous terms dictated by the troika (i.e., the European Central Bank, European Commission and International Monetary Fund) -- since his rise from local political operator to international political icon in the wake of the country's inconclusive parliamentary elections on May 6, it appears extremely unlikely Syriza would be joining such a coalition with the likes of either New Democracy or Pasok any time soon.
Meanwhile, representatives of the euro zone's paymaster, Germany, appeared happy with the Greek election results.
The German federal government would consider such a result a decision by Greek voters to forge ahead with the implementation of far-reaching economic and fiscal reforms, German Finance Minister Wolfgang Schaeuble said in a statement quoted by Reuters.
And German Foreign Minister Guido Westerwelle even indicated Greece might be given more time to comply with certain of the austere terms of the €240 billion ($300 billion) in bailout loans dictated by the troika, as he said on German TV station ARD, There can't be substantial changes to the agreements, but I can imagine that we would talk about the time axes once again, given that in reality there was political standstill in Greece because of the elections, which the normal citizens shouldn't have to suffer from.