LOS CABOS, Mexico — European leaders appealed for patience from the world as they came under increasing pressure after market relief from the Greek election proved short-lived and Spain came under renewed financial strains.

The presidents of the European Commission and European Council, in a news conference shortly after the opening of the G-20 summit, insisted that Europe has the political will to fix the continent’s debt crisis. They said they were encouraged by the Greek vote outcome, and indicated a willingness to help Athens, once a governing coalition is formed, to hit financial targets to meet its bailout obligations.

At the same time, the European leaders also sought to turn some of the spotlight to other nations, saying Europe wasn’t the only party in the G-20 that had financial and debt issues to work out. European officials hope they can reassure global markets and leaders when they meet June 28 for a summit in which they are expected to lay out plans for a banking union and other steps to strengthen integration and reduce economic imbalances.

“Certainly we are not coming here to take lessons from nobody,” said Jose Manuel Barroso, president of the European Commission, the executive arm of the 27-nation European Union. He reminded people that Europe was not the origin of the global financial crisis and that unlike some other countries in the G-20, which he did not name, Europe functioned as a democracy. With 17 nations in the eurozone, he said, “sometimes it means taking time” to agree to policy actions.

Moreover, he called on non-European G-20 member nations to fulfill their commitments to pony up money for a bailout fund for the International Monetary Fund. Europe has pledged to put in more than half of the $430 billion additional IMF firepower recently announced. “Others unfortunately aren’t on time,” Barroso said.

Barroso’s at-times defensive remarks, echoed with less emotion by European Council President Herman Van Rompuy, reflected the heat the European leaders are feeling here from the heads of other major countries, whose economies are hurting from persistent financial shocks from Europe. One by one, they are urging their European counterparts, who occupy five of the 20 G-20 seats, to act decisively to resolve the debt crisis, now in its third year.

President Barack Obama joined other G-20 leaders in expressing greater confidence after the Greek elections Sunday, and suggested that European leaders ease the stringent austerity requirements that have had a punishing effect on the Greek economy and provoked rebellion among many citizens.

“I think the election in Greece yesterday indicates a positive prospect for not only them forming a government,” Obama said, “but also them working constructively with their international partners in order that they can continue on the path of reform, and do so in a way that also offers the prospects for the Greek people to succeed and prosper.”

But investor enthusiasm that Greece might have averted an immediate exit didn’t last long, and Spain’s borrowing costs rose Monday again, to dangerously high levels, threatening another escalation of the eurozone crisis.

Leaders of the G-20, which represents almost 90 percent of the world economy, have played down expectations that the summit will yield new concrete actions or plans to ease the debt crisis. European leaders hope that they can reassure global markets and leaders when they meet June 28. But Van Rompuy said Monday that people shouldn’t expect decisions to be made at the end of the month. And he ruled out any short-term action on a proposal to share the debt risk with eurobonds, saying that Europe doesn’t have the requisite mechanisms and economic balances in place to support such debt-sharing anytime soon.

“We understand the problems of others,” he said. “Please understand ours.”