Dow Jones industrial average futures were up 40 points early Monday morning, suggesting the market could open higher.
Japan's Nikkei 225 stock index was up about 2 percent. The euro rose above $1.27 from $1.26 late Friday in New York.
The presidents of the European Council, representing the heads of state or government of the 27 European Union members, and the European Commission, the EU's executive body, issued a joint statement after Greece's election saying, "We are hopeful that the election results will allow a government to be formed quickly."
"We will continue to stand by Greece as a member of the EU family and of the euro area," Herman Van Rompuy and Jose Manuel Barroso said in their statement issued from Los Cabos, Mexico, on the eve of the Group of20 summit of the leaders of the world's most powerful economies.
"We look forward to working with the new government and to support the continued efforts of Greece to put its economy on a sustainable path," the statement said.
The center-right New Democracy won the election with 30 percent of the vote and 128 seats in the 300-seat Parliament, unofficial results indicated.
The Coalition of the Radical Left parliamentary group, known as Syriza -- which had surged on a wave of anti-austerity sentiment with promises of tearing up Greece's loan agreement with its foreign creditors -- came in second, with 27 percent of the vote and 72 seats.
The Panhellenic Socialist Movement, or Pasok, placed third, with 12 percent and 33 seats.
The extreme right neo-Nazi Golden Dawn party came in fourth, with 6.9 percent and 18 seats.
"There is no time for political games. The country must be governed," New Democracy leader Antonis Samaras, in line to become prime minister, said in a post-election news conference.
"We will cooperate with our European partners to boost growth and tackle the torturous problem of unemployment," he said and called on other parties to join him in a "national salvation" coalition government.
Greece has 22 percent unemployment.
Alexis Tsipras, the 37-year-old Syriza leader, conceded defeat but said his group would not be part of a coalition.
"We fought against blackmail to put an end to memorandum," he said, referring to the loan agreement. "We're proud of our fight."
He said Syriza would be "present in developments from the position of the main opposition party."
German Chancellor Angela Merkel called Samaras to congratulate him.
At the same time, her office said she "expected Greece to stick to its European commitments," while Finance Minister Wolfgang Schauble said in a statement there would be consultations to "work toward making the adjustment program succeed."
German Foreign Minister Guido Westerwelle said separately on German TV broadcaster ZDF, "I could imagine that we do something about the time frame" for Greece's debt payments.
European leaders have insisted Greece find $15 billion in fresh budget cuts by the end of this month.