Frank-Walter Steinmeier said it was a contradiction of comments made days ago by Mr Trump's incoming defence chief.

In an interview in New York, Mr Trump also said Germany's Angela Merkel made "a catastrophic mistake" by admitting more than one million migrants.

And he threatened German car makers with high import tariffs.

Companies including BMW, Volkswagen and Daimler have invested in factories in Mexico, where costs are cheaper, with an eye to exporting into the US market.

But Mr Trump said: "I would tell them to not waste their time and money unless they want to sell to other countries. That would be ok, if you want to build in Mexico.

"I would tell BMW, if you want to build a factory in Mexico and sell cars to the US without paying a 35% tax, forget it."

Mr Trump was giving details of his foreign policy goals in an interview with British and German newspapers, the Times and Bild, at Trump Tower in New York.
Anger and dismay, but not surprise: BBC Berlin correspondent Jenny Hill

Donald Trump's comments have caused dismay, concern - but perhaps not surprise - in Berlin. Few expected the new transatlantic relationship to echo the warm and trusting alliance nurtured by Angela Merkel and Barack Obama, who was a vocal supporter of Mrs Merkel's refugee policy.

There is anger, too. Germany's outspoken Vice-Chancellor Sigmar Gabriel retorted that the migrant crisis was the result of "faulty, interventionist American policies in the Mediterranean and Middle East".

That Mr Trump should take aim at Germany's car manufacturers has also raised eyebrows, though few here believe his congress would approve the 35% tax he appears to be threatening to impose on imported vehicles.

Germans were largely unimpressed by Mr Trump during his election campaign and now, despite his own German heritage, the president-elect is doing little to endear himself.

On Nato, Mr Trump reiterated his criticism that "a lot of" the 28 member states were not paying their fair share.

He said the alliance had been forged "many, many years ago", adding: "It's obsolete because it wasn't taking care of terror.

"And the other thing is the countries aren't paying their fair share so we're supposed to protect countries. But a lot of these countries aren't paying what they're supposed to be paying, which I think is very unfair to the United States."

In an apparent contradiction, Mr Trump then said Nato was "very important" to him.

What will Trump's foreign policy look like?

Speaking later in Brussels, Mr Steinmeier said the president-elect's comments had caused "worry and concern".

"I've just had a conversation with the Secretary-General of Nato, Jens Stoltenberg, who has expressed concern at the comments made by Donald Trump that Nato is obsolete," he said.

"This is in contradiction with what the American defence minister said in his hearing in Washington only some days ago and we have to see what will be the consequences for American policy."

At his Senate confirmation hearing last week, Mr Trump's choice for defence secretary, Gen James Mattis, described Nato as central to US defence.

And he accused Russian President Vladimir Putin of trying to "break" the alliance.

A Kremlin spokesman said on Monday that Russia agreed with Mr Trump's evaluation of Nato, particularly that it had become obsolete, Russian news agency Interfax said.

Trump's interview: Key points

    Brexit: It was a "smart" decision by the UK
    UK-US trade deals: "We're gonna get something done very quickly"
    Angela Merkel: She made a "catastrophic mistake" by letting in a million migrants
    The EU: "It's basically a vehicle for Germany" and other countries will also leave because of anger over immigration
    Nato: It's "obsolete" but "very important to me" and other members should pay "their fair share"
    Iran nuclear deal: It's "one of the dumbest deals I have ever seen"
    Iraq war: It was "like throwing rocks into a beehive"
    Twitter: "I'll keep it [as president] - I can go bing, bing bing" and respond to "dishonest" news

Mr Trump described German Chancellor Angela Merkel as Europe's most important leader, but said that the EU had become a vehicle for Germany.

He also said Mrs Merkel had made a "catastrophic mistake" by admitting more than one million migrants and refugees.

"I think she made one very catastrophic mistake and that was taking all of these illegals... And nobody even knows where they come from," he added.

Asked about Mr Trump's comments, Mrs Merkel told reporters in Berlin that Germany would wait until after his inauguration and then work with the new administration to see what kind of agreements could be achieved.

Mr Trump linked the migrant issue with Brexit - the UK referendum vote to leave the EU.

He promised a quick trade deal between the US and the UK after he takes office on Friday.

However, a European Commission spokeswoman has reiterated that the UK will not be allowed to engage in formal talks involving a trade deal with the US until 2019, when it has finished the process of leaving the EU.

A senior figure in Chancellor Angela Merkel's Christian Democratic Union (CDU) said Mr Trump's comments on the EU were creating a false picture.

"It seems that some people have the impression that the EU is about to unravel...[that] after Britain, others will leave too," said Jens Spahn.

"That's a false picture of the EU and also of what it does."