LOS CABOS, Mexico — Needing an economic boost, President Barack Obama is trying to land assurances that Europe is closing in on a financial crisis response that will calm the markets and keep the continent’s woes from undermining the world. As he presses European leaders to drum up economic demand, they want promises the United States won’t plunge off a fiscal cliff by year’s end.

Obama, as leader of the giant but struggling U.S. economy, remains central to the Group of 20 summit talks wrapping up today in this coastal resort region. But it is the European members gathered here, led by Germany and its chancellor, Angela Merkel, who carry both the power and responsibility to stabilize a eurozone reeling from debt, banking and political problems.

Obama sent some upbeat signals Monday amid a sense of global relief that Greece, based on new elections, would not renege on its bailout terms and ditch the euro currency. Obama left a meeting with Merkel feeling “encouraged” about Europe’s direction, a spokesman said, as an even more consequential European summit on the crisis approaches in Brussels.

Europe’s ability to turn around its fortunes fast will have direct bearing on whether Obama wins a second term. The bigger the drag from abroad, the harder the job growth in the United States.

Obama said all countries must “make sure that we’re contributing so that the economy grows, the situation stabilizes, confidence returns to the markets, and most importantly, we’re giving our people the chance if they work hard to succeed and do well.” After lobbying for Greek voters to stick with budget reforms and the euro, he called their election results a “positive prospect.”

Obama was spending much of today on the economic crisis after taking care of some unrelated diplomatic business — his first meeting with Vladimir Putin since the former Russian president returned to the job this year. The leaders met for two hours Monday, in talks dominated by a bloody Syrian conflict that has deeply divided Russia and the U.S.

Obama has set up private talks with one other leader, Chinese President Hu Jintao, today before closing off his summitry with a news conference in the late afternoon.

Central to the G-20 debate is how nations can boost jobs and consumer demand without sinking deeper into debt. Obama has implored governments to spend and grow, not just cut.