At a Group of 20 summit of the world's leading industrialized and developing economies in this Mexican resort, Germany and its big euro zone partners took the unusual step of spelling out in detail measures to complete the economic and monetary union they launched to great fanfare 13 years ago.

Among the commitments in a draft G20 communique was a pledge to consider concrete steps towards a "more integrated financial architecture" in Europe that would include common banking supervision and firm guarantees to repay bank depositors.

The United States, the International Monetary Fund and European Commission have been urging EU member states to press ahead with a banking union to break the vicious link between deeply indebted governments bailing out illiquid financial institutions, worsening the sovereign debt problems and deepening the euro-zone crisis.

While that term did not appear in the declaration, the wording did suggest that Germany, which has rejected initiatives that might expose it to the cost of rescuing banks outside its borders, was growing more open to the idea of closer banking cooperation.

U.S. President Barack Obama, concerned that Europe's debt crisis could deteriorate further and upend his re-election hopes, met with Chancellor Angela Merkel, who as the leader of Europe's biggest economy is under intense pressure to commit German resources to underpin the euro zone and prevent a catastrophic breakup.

Obama's spokesman said the U.S. president was encouraged by the talks, which touched on steps to "increase European integration".

EU President Jose Manuel Barroso showed frustration over the pressure which is piling on Europe to act fast. He said G20 members must understand it will take time for the 17 euro zone democracies to agree on how to build a full financial, fiscal and political union and asked fellow G20 members to stop lecturing.

"We certainly are coming here to receive lessons from nobody," he said.

BOOSTING GROWTH

Protected by Mexican navy vessels and troops who patrolled sun-baked beaches and highways, leaders from the G20 countries representing more than 80 percent of world output agreed to prioritize boosting growth and job creation, hit hard by the focus on sharp budget cutbacks, which has contributed to an accelerating slowdown in the global economy.

The World Bank last week lowered its forecast for global growth in 2012 to 2.5 percent and said developing nations faced a long period of financial market volatility and weaker growth.

In its strongest signal in three years that it would act to strengthen the recovery, the G20 said in their draft communique that countries without heavy debts problems were ready to act together to spur growth, if the economy slows a lot more.

The United States has pressed Germany as well as China to stimulate spending in order to help the world economy.

Rising violence in Syria and the near-collapse of a United Nations-brokered peace plan was also in focus as U.S. President Barack Obama met with Russian President Vladimir Putin. The two super powers have clashed over arming Syria and U.N. sanctions.

Obama and Putin agreed that the violence in Syria has to end but offered no new solutions and showed no signs of reaching a deal on tougher sanctions against Damascus.

RELIEF RALLY FLEETING

Europe's battle against a debt crisis that has led Greece, Ireland and Portugal to seek EU/IMF rescues, and forced Spain to seek aid for its banks, dominated the opening discussion of G20 leaders on the global economy.

A narrow victory for the conservative New Democracy party in the Greek election on Sunday eased concerns the heavily indebted country could exit the euro zone soon. But it did little to calm financial markets, which fear a euro zone breakup has only been delayed and will drag Spain and Italy into the maelstrom.

"The win in Greece does not really resolve anything," said Boris Schlossberg, managing director at investment advisory firm BK Asset Management in New York. "It's still going to be tough for Greece."

Fitch Ratings agency said the Greek result had lowered the risk of a disorderly default and the scenario of a euro zone exit, but it also warned that any new government in Athens was likely to be fragile.

After an initial relief rally, the euro fell against the dollar. Spanish bond yields hit a new euro-era high above 7 percent.

Merkel, speaking to reporters after landing on the southern tip of Mexico's Baja California peninsula in the middle of the night, welcomed the Greek result but said she could not accept any loosening of the austerity measures and deep structural reforms Athens has agreed to as a condition of its two EU/IMF bailouts totaling 240 billion euros.

"The Greek government will and must deliver on the commitments it has agreed to," she said.

That puts her on a collision course with the winner of the Greek vote, conservative Antonis Samaras, who campaigned pledging to renegotiate elements of the rescue and reiterated that stance on Monday, saying "amendments" were needed to relieve "crippling unemployment and huge hardships" for Greeks.

Greece will ask to spread 11.7 billion euros in austerity cuts over four years instead of two, a New Democracy party source told Reuters in Athens.

German frustration with Greece's failure to deliver on its reform pledges has risen in recent months, as has Greek anger at the tough austerity prescribed by Berlin and its partners.

In a twist of fate, Greece's soccer team will battle Germany later this week in the quarter-finals of the European championships.

David Mackie, an economist at JP Morgan, said he expected European governments would ultimately be forced to agree to an "aggressive restructuring" of the loans they have already provided to Greece to return the country to a sustainable path.

EXTRA IMF FIREPOWER

Merkel has been pushing fellow European leaders to agree a road map toward closer fiscal integration that would involve ceding sovereignty over budgets to Brussels and giving more power to the European Parliament.

By sketching out what the bloc might look like in five to 10 years, she hopes to win back the confidence of markets.

But her counterparts, notably new French President Francois Hollande who arrived here later on Monday after his Socialist Party won control of the French parliament in weekend elections, have doubts about transferring fiscal powers. It appears unlikely that Europe will deliver a "grand bargain" at a separate summit of EU leaders on June 28-29.

In Los Cabos, leaders are set to confirm they will double the IMF's firepower. The Fund's managing director Christine Lagarde said pledges now totaled $456 billion, up from the $430 billion in April, even though some emerging nations are frustrated with the slow pace of winning more power at the global lender.

China on Monday offered to contribute $43 billion to the IMF's crisis-fighting reserves, adding to offers of $10 billion each from Brazil, Russia and India.

(Additional reporting by G20 team in Los Cabos, and Gertrude Chavez-Dreyfuss in New York.; Writing by Noah Barkin and Stella Dawson; Editing by William Schomberg and Padraic Cassidy)

• A Permanent Economic Emergency