Åkesson says that his party has some things in common with France's far-right national Front, and Marine Le Pen is the candidate he prefers. She faces liberal Emmanuel Macron in the second round, after coming second.
Åkesson also says that if she does well it would be a real bloody nose for the European Union, and he hopes this would mean changes for Sweden as well. His party would like to hold a referendum on Sweden leaving the EU.
And on the left Jonas Sjöstedt wrote on Twitter that it had been a "historic success" for the person who's been called France's Bernie Sanders, Jean-Luc Mélenchon, who seems to have scored about 19 per cent.
The leaders of other Swedish parties, from the Social Democrats, to the Moderates, Liberals, Center Party and Greens, have all praised Emmanuel Macron, who is expected to beat Le Pen in the second round, and combines a social liberal platform with market reforms. He is seen as the open candidate, facing a rival who emphasises nationalism.
Swedish Foreign Minister Margot Wallström congratulated him, telling Sweden's TT newswire that her government believed in "cooperation based on democratic values, a strong EU, free trade, and an open, tolerant society".
Anna Kinberg Batra, leader of the Moderate Party, said that a Macron victory in the second round would be "best both for France and for us."
"Macron has clearly stated that he wants to engage in European cooperation and that work together constructively with other countries," she said.
"If he were voted in, his most important task will be to succeed in creating growth and jobs in a France facing serious problems."