It was early Thursday morning in the Belarussian capital of Minsk when German Chancellor Angela Merkel emerged, looking sober and weary, after an all-night negotiating session.

Over the prior week, she had held talks with her counterparts in Kiev, Moscow, Washington and Ottawa, a diplomatic obstacle course that culminated in an agreement for a ceasefire in Ukraine. Within hours of reaching the agreement in Minsk, she flew to Brussels for a summit with European leaders as time runs out to reach a solution to Greece's debt impasse.

It's little wonder, then, that Germany's tabloid Bild recently described Ms. Merkel as "The World Chancellor." In many ways, this is Ms. Merkel's moment. After a decade in power, she is facing two defining crises – the violence in Ukraine and the clash over Greece's debt. At the heart of how she is tackling both problems is a conviction that Europe is better off united, a belief born of her own Cold War experience.

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Ms. Merkel's appearance centre stage comes with risks. No world leader has invested more time or energy in seeking a negotiated solution to the war in Ukraine. But if the current agreement collapses just as the previous ceasefire deal did, it will deliver a blow to her steady, diplomatic approach and strengthen those who say military aid is necessary to check Russian aggression. It could also open a rift between the United States and Europe.

The Chancellor's growing prominence is a reflection of Germany's changing role on the world stage. The country is now unquestionably – albeit reluctantly – the leading power in Europe. For now, at least, Germans appear proud of Ms. Merkel's dogged pursuit of her policy aims. "Merkel, go ahead!" read a headline Friday in Die Zeit, a leading daily. "In the front against Putin, it's no longer the United States but the European who dominates. This new task requires courage."

In some ways, Ms. Merkel's no-nonsense, no-frills style is well suited to the current predicaments. "She forbids herself to be emotional about things she can't change," said Stefan Kornelius, author of a recent biography of Ms. Merkel. "And she definitely can't change foreign leaders."

Instead, she accepts what's in front of her and gets down to business, he said, whether with Russian President Vladimir Putin or Greece's new prime minister Alexis Tsipras.

Since the Ukraine crisis began, Ms. Merkel has talked on the phone with Mr. Putin more than 30 times, a number that speaks to her stamina and persistence, as well as her conviction that there is no military solution to the conflict. By November, though, even the indefatigable Ms. Merkel appeared to lose her patience with the Russian leader. Yet by earlier this month, she was shuttling around the globe, racing to assemble the initiative that, after 17 hours of talks, produced the current ceasefire agreement.

Her background informs her approach to her current challenges. She believes strongly in the post-Cold War order in Europe where nations have the freedom to determine their own destiny. But she also is convinced that a resolution to the Ukraine crisis can only be achieved through dialogue and economic pressure.

Last week, she recalled how, as a seven-year-old, she saw the Berlin Wall go up in 1961. She noted that no one seriously considered using force to tear it down. Instead, East Germans endured decades of dictatorship before various pressures managed to topple the Wall.

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Similarly, in Ukraine, the bitter reality is that the conflict cannot be won with weapons, she said. "I cannot imagine any situation in which improved equipment for the Ukrainian army leads to President Putin being so impressed that he believes he will lose militarily," Ms. Merkel said, according to the Associated Press. "I have to put it that bluntly."

Ms. Merkel knows the confrontation with Russia "is not something that will be settled or ended any time soon," said Joerg Forbrig, an expert on Eastern Europe at the German Marshall Fund of the United States. "We need to stay away from seemingly appropriate short-term measures like arms support to Ukraine, which only have explosive potential."

A spokesman for Ms. Merkel did not respond to a request for comment on her new global stature or the potential consequences of a failed ceasefire in Ukraine.

Even in Germany, Ms. Merkel remains a subject of fascination. In private, those who know her say, she is funny, cynical and highly inquisitive. At 60, she has led Germany for almost 11 years, never deviating from her calm style and meticulous analysis of political problems, which some ascribe to her training as a quantum chemist. She is married to a fellow scientist, has no children, lives modestly in central Berlin and loves soccer.

Some have nicknamed her "mutti" – or mommy – often as an insult rather than a compliment, but either way it's an image that doesn't quite fit. Nor is she "the handbag-swinging Margaret Thatcher type," Mr. Kornelius said. "She's just Merkel."

Ms. Merkel's unique way of doing things is a combination of caution and ambition. The daughter of an East German pastor, she was an anomaly in the centre-right Christian Democratic Union party, which was dominated by male politicians from the former West. On her route to the top, she showed she could be ruthless, pushing aside her mentor Helmut Kohl, who presided over German reunification.

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Critics sometimes label her approach "Merkiavellism," saying she seeks above all to remain electable, preferring to contain crises and maintain stability rather than seek solutions. However you describe her method, it's a way of doing things that resonates deeply among German voters. Currently Ms. Merkel's approval rating hovers near 70 per cent, a remarkable figure for any politician, let alone one who has been in power this long.

Ms. Merkel's current term, her third, expires in 2017 and she has not said whether she will run again. If she does serve out a fourth term, she would become one of only two chancellors in post-war Germany to achieve that feat. Some have speculated Ms. Merkel might have other goals in mind. For instance, a new Secretary-General of the United Nations is likely to be selected in 2016, they note. According to that conjecture, Ms. Merkel might just end up "World Chancellor" after all.