AMNA NAWAZ: In Berlin today, Friedrich Merz was elected Germany's chancellor, but not without a surprising setback.

For the first time in Germany's modern history, he lost the Parliament's initial vote and needed a second round to secure a majority.

Nick Schifrin is back now with this report on the challenges that Merz inherits, from a politically divided Germany to an American president who's questioned the transatlantic alliance.

NICK SCHIFRIN: Today, in Germany, a bitter victory.

Friedrich Merz became Germany's 10th post-World War II chancellor and the first to lose an initial secret round of voting.

Merz had promised to begin his chancellorship forcefully and today showed the fragility of his leadership and coalition.

But, this evening, at the official handover ceremony without going Chancellor Olaf Scholz, Merz brushed it aside.

FRIEDRICH MERZ, German Chancellor (through translator): Today, what a day with a few surprises.

I accept this responsibility with humility but also with determination and confidence.

NICK SCHIFRIN: Wolfgang Ischinger is the longtime former chairman of the Munich Security Conference and the former German ambassador to the U.S. and U.K. WOLFGANG ISCHINGER, Chairman, Munich Security Conference: When I look at foreign policy, security and defense, I see a government being formed today in Berlin which is going to have a very, very solid background.

DONALD TRUMP, President of the United States: You're gambling with World War III.

NICK SCHIFRIN: Merz's international challenges begin with an American president who's fought openly with European leaders.

To this moment, Merz reacted with horror.

FRIEDRICH MERZ (through translator): In my opinion, it was not a spontaneous reaction to interventions by Zelenskyy, but obviously a triggered escalation.

NICK SCHIFRIN: When Vice President Vance lectured Europe on democracy in Munich... J.D.

VANCE, Vice President of the United States: What German democracy -- what no democracy, American, German or European, will survive is telling millions of voters that their thoughts and concerns, their aspirations, their pleas for relief are invalid.

NICK SCHIFRIN: Merz imagined a Europe without an American alliance.

FRIEDRICH MERZ (through translator): For me, the absolute priority will be to strengthen Europe as quickly as possible so that step by step we can really achieve independence from the USA.

It's clear the Americans, or at least this group of Americans, this government, cares very little about the fate of Europe.

DONALD TRUMP: So, maybe they're not our allies, right?

NICK SCHIFRIN: And to President Trump's questioning the longevity of transatlantic alliances, Merz questioned the reliability of the U.S. promise to defend Europe with nuclear weapons.

FRIEDRICH MERZ (through translator): We must be prepared that Donald Trump will no longer fully accept the promise of assistance under the NATO treaty.

WOLFGANG ISCHINGER: Yes, Friedrich Merz, has expressed, as most other Europeans have done, serious concerns about the reliability, the credibility of the American position in NATO, about America's changing, evolving positions on Ukraine.

The good news is that Friedrich Merz, the new German chancellor, and Donald Trump have not worked together in the past, and they have not had any reason to disagree in the past.

NICK SCHIFRIN: But Merz's most pressing problem after today is perhaps domestic.

The leading opposition party is the far right AfD, or Alternative for Germany.

AfD is anti-immigrant and its leaders have been accused of making anti-Muslim, antisemitic and antidemocratic statements.

But last week, after the German intelligence agency labeled AfD extremist, Secretary of State Marco Rubio -- quote -- "That's not democracy.

It's tyranny in disguise."

The German Foreign Ministry rebuked him: "We have learned from our history that right-wing extremism needs to be stopped."

But the AfD is polling ahead of Germany's traditional parties.

It was excluded from the coalition government and today called Merz weak.

BERND BAUMANN, Representative, AfD Party (through translator): This government starts out in extreme instability and it will remain unstable.

WOLFGANG ISCHINGER: That's got to be the important, number one goal for this new coalition government, to make sure that traditional conservative voters will leave their frustration behind and will find it acceptable and normal to vote for the classic conservative government led by Friedrich Merz, and not out of frustration or despair for the right-wing party.

NICK SCHIFRIN: Do you believe that this issue will continue to increase tensions between the U.S. and Germany?

WOLFGANG ISCHINGER: One of the points that some of my American friends have not sufficiently understood is that the AfD, which has been befriended by some here in Washington, is, of course, a totally anti-American political party.

NICK SCHIFRIN: The far right and a stagnant economy await Merz.

But, tonight, he expressed relief that at least he survived the day.

For the "PBS News Hour," I'm Nick Schifrin.