U.S. President Donald Trump and German Chancellor Angela Merkel Ukas Michae/Pool/Getty Images

Berlin might be over 4,000 miles away from Washington DC but Sunday's election in Germany and forthcoming negotiations over a future coalition government will be closely monitored in the U.S. capital. Analysts, however, predict that the "world views" of U.S. President Donald Trump and German Chancellor Angela Merkel will remain at odds. , with 33 percent, although it lost a lot of ground to the far-right, anti-immigrant and anti-euro party Alternative for Germany (AfD), which garnered 12.6 percent of the vote and is to enter the German parliament for the first time. Domestically, and in Europe, the coalition parties that form a government could determine how much Germany is willing to support ever closer political and economic union in the euro zone (the FDP is not keen). On an international level though, Merkel's foreign policy stance towards the U.S. – one of trying to get Washington to stick to an international climate agreement drawn up in Paris in 2016 and maintaining transatlantic trade and investment – is likely to stay the same, analysts and diplomats noted.

Peter Wittig, German Ambassador to the United States, told CNBC on Monday that Merkel had a "clear mandate to form the government" and that her re-election meant continuity. "There will be a lot of continuity in Germany's role in Europe and the world. The chancellor has said she wants to continue her successful economic policies of ... free trade and she has clear view of reforming the European Union, so there will be a lot of continuity and, of course, Germany will be a very reliable partner to the U.S." Chris Scicluna, executive director and head of Economic Research at Daiwa Capital Markets Europe agreed that while the election will eventually result in a new coalition government for Merkel, "it seems unlikely to change much in terms of German economic or foreign policy." "So, for example, in marked opposition to the Trump world view, Merkel's foreign policy will be very much centered on supporting global institutions, while she will also remain at the forefront of defining a common European response to geopolitical challenges," Scicluna said. "And with the Greens likely to be on board, Merkel is hardly going to dilute her support for anti-climate change policies such as the Paris Accord."

Clash of world views

So far, Merkel's diplomatic relations with Trump have been reserved at best and their stances on trade, climate change and immigration are poles apart – with Trump advocating an "America First" policy, denying climate change and calling for strict immigration bans in the U.S. For his part, Trump has been characteristically vocal in his criticism of Merkel's move to allow over one million refugees to enter Germany in 2015 at the height of the region's migrant crisis, calling it a "catastrophic decision." That there's no love lost between the powerful politicians has not been lost on experts. "The relationship between the two of them is not good, but this does not affect the close institutional relationship between the two countries," Charles Linchfield, associate at political risk consultancy Eurasia Group, told CNBC Monday. "(But) in general terms this election reminds us that Merkel is a leader of one country and has her own domestic muddles to get through. She doesn't have the time or resources to be the 'leader of the free world' and so she is still dependent on the U.S.'s military and even economic leadership," he added.

Nonetheless, Merkel's stance towards Trump could also be influenced by her governing partners, according to Ricardo Garcia, head of European Macroeconomics at UBS, with particular mention going to the Greens who, unsurprisingly, would not be impressed with any U.S. withdrawal from an international agreement to limit global warming. Garcia told CNBC in an email Monday that the Greens would be likely to remain 'Trump-skeptic' particularly given their environmental credentials. Having said the Paris agreement was a "bad deal," Trump's administration is currently considering whether or not to withdraw from the accord. In addition, Garcia thought the Greens would pressure any potential coalition to increase spending on defense in line with Trump's insistence that NATO members should spend at least 2 percent of their gross domestic product (GDP) on its own defense per year.