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Greek Prime Minister Alexis Tsipras is shown leaving the eurozone summit meeting at European Union headquarters in Brussels, on July 7, 2015. JOHN THYS/AFP/Getty Images

A July 6-10 poll from YouGov found that the majority of people it surveyed in six European countries were softening their positions on the Greek debt crisis. The U.K. and France showed the most support for Greece, while Germany as well as Nordic nations such as Sweden, Denmark, and Finland were the toughest, with the general trend across all nations showing declining support for a Grexit.

The question of a Grexit -- meaning Greece would leave the common currency of the eurozone -- began to be discussed in earnest by European nations following Greece's default on a $1.76 billion payment to the IMF on June 30. The payment was part of a larger bailout plan put in place by the IMF, the European Central Bank, and the European Union following the global recession almost five years ago.

In the U.K., 39 percent of those polled were in favor of renegotiating Greece's debt, as were 38 percent in France. Comparatively, only 16 percent of Germans were amenable to debt renegotiation and only 14 percent of Finns were.

The percentage of Germans wanting Greece to leave the eurozone was down to 47 percent, compared to 53 percent on June 25. Thirty-seven percent of Germans now responded as actively wanting Greece to stay in the eurozone, which is up from only 29 percent on June 25. These new results come from poll data taken after the Greek referendum on July 5, in which the majority of Greeks who went to the polls voted against more austerity measures.

European citizens across the continent have been divided along the fault lines of pro-austerity or anti-austerity when it comes to Greece, and this poll data could indicate a shift toward a more moderate stance regarding debt restructuring.

This data is increasingly relevant as Greek Prime Minister Alexis Tsipras continues to make the case for his new bailout program in the European Parliament. Tsipras presented his new plan today, and it includes a bailout of 53.5 billion euros in exchange for deep cuts in Greece's budget.

YouGov polled from 1,002 to 1,756 people per nation. It was immediately unclear what the percent for margin of error was.