Earlier this month, the Finnish conductor Osmo Vänskä came to South Florida with his Minnesota Orchestra and the violinist Midori, who played the Sibelius Violin Concerto.

They played the Knight Concert Hall, but I caught them in West Palm Beach, and it was sensational. Vänskä is without any doubt one of the finest conductors working today, a director who is able to rethink each of the pieces he played so thoroughly that even a chestnut, such as the Beethoven Fifth Symphony, sounded almost as though it were newly composed.

On Saturday and Sunday, he’s back in South Florida to appear with the New World Symphony in two programs of Nordic music, including that same Sibelius concerto, this time with the young Norwegian violinist Henning Kraggerud as the soloist. The program also contains a new piece of Finnish music, Minea, written in 2009 for the Minnesota Orchestra (hence its name) by Kalevi Aho, and the Fourth Symphony (The Inextinguishable) by the great Danish composer Carl Nielsen.

Vänskä said he’s worked with Kraggerud once before in London, when the young violinist performed the six Humoresques of Sibelius, a little-known collection of showpieces. “He really played well,” Vänskä said Wednesday. “And therefore I also wanted to do the concerto and thought that now it’s time to do that together with him.”

In the Minnesota Orchestra performance, Vänskä opened the concerto with an astonishingly soft reading of the first measures, which consist of high string tremolos before the entrance of the soloist. Vänskä said he makes a point of stressing soft dynamics.

“I think it always pays to go softer. Sometimes we like to play louder and louder and louder, but there is a limit; you can’t play louder,” he said. “But if we are able to go softer, that makes the range larger. That same fortissimo sounds louder if the softer part is really soft. That’s what I always try to do. And it’s hard to play soft. It takes some work, and it’s not easy.”

And taking care to draw that kind of contrast helps in music like the Sibelius concerto, which is “very atmospheric,” Vanska said, adding that the composer had a specific instruction in mind for the kind of feeling he was trying to create in the opening.

“Sibelius said that it should be like an eagle that’s flying: The bird can see all the details, but also the big picture,” he said. “And I like this idea very much, because if we think about the eagle, it doesn’t need to be fast. There is always an authority that’s there … and what the orchestra should be doing is trying to create an atmosphere of air and maybe a little bit of sunshine.”

Minea (here are the final four minutes, with Vänskä and the Lahti Symphony of Finland) is a showpiece for the orchestra that Vänskä has been called “Aho’s Bolero,’’ like the famous Ravel essay in orchestral color, rhythm and dynamics.

Vanska said the first half is like “African folk music,” and has percussion playing very quietly, but that the second gets stronger and louder and more percussion-heavy, like the Ravel. It also features a prominent solo for the contrabassoon, a huge, difficult instrument to play that almost always plays a supporting role, adding some subterranean color to the bass.

“I have conducted it in many places, and the audience usually likes it very much. Also, the players of the orchestra like it,” he said. “It’s a complicated piece, as always with Mr. Aho’s music, but when we can play it well enough, it sounds really good.”

Then there is the Nielsen Fourth, a masterpiece of early 20th-century symphonic writing that is heard far too infrequently.

“He is a totally underestimated composer. His music is very powerful and has its own musical language,” Vänskä said. “I have heard so many times after a concert where some of his pieces were played, the audience members saying, ‘I really liked it, but I hadn’t heard it before.’”

Vänskä said, “there is no reason to be scared” of Nielsen’s music, for those who are unfamiliar with it. And the Fourth, completed in 1916, has some strong extramusical associations with the First World War in the form of a “battle” between timpanists on either side of the stage.

“Sibelius had many challenges for the performers, but Nielsen’s music is really complicated … the conductor should be very familiar with it in order to be able to do it,” said Vänskä, who has conducted all six Nielsen symphonies with the Minnesota Orchestra. “And it’s difficult for the players. I am really, really happy that the New World Symphony wanted to do that piece, because it’s the kind of repertoire for those young players that they can use later.”

Vänskä’s contract with the Minnesota Orchestra runs through 2015, and he says he enjoys living and working there, not just because Minnesota itself has a strong connection to the Nordic countries, but because it’s a “very culturally friendly area.”

And, of course, he loves his band.

“The Minnesota Orchestra is a great orchestra which always tries to do things better and better,” he said. “They are ready to try anything I ask them to do.”

Which is a good thing for classical music in general.

“We are living in very hard times, and financial challenges are huge. But I think there is always a future for classical music. As performers, we have to take care that we are playing always at the highest possible [level],” Vanska said. “It a little bit like sports teams. If a team is just losing, not winning, then who would like to come and follow it? It’s the same thing with the orchestra. If we are playing really well, and people have a good reason to come listen to us, then we have a future there.

“If we don’t play well, then we have to ask ourselves first: ‘Why do we do this, if we are not giving our heart, if we are not giving our energy, for these performances?’”

Osmo Vänskä conducts the New World Symphony and violinist Henning Kraggerud at 8 p.m. Saturday and 2 p.m. Sunday at the New World Center in Miami Beach. Tickets start at $28; Saturday night’s concert already is sold out. Call 305-673-3331 or visit www.nws.edu.