Danish ALDE candidate for the European Commission Presidency Margrethe Vestager gives a speech in Brussels on May 26, 2019 | John Thys/AFP via Getty Images Danish PM swings behind Vestager for EU top job Danish competition boss could be a compromise to head the European Commission.

Danish Prime Minister Lars Løkke Rasmussen has given a strong signal that Copenhagen would push for Competition Commissioner Margrethe Vestager to take the EU's top job.

Rasmussen, who has previously been cool on his old political sparring partner Vestager, described her as "the best candidate" to succeed Commission President Jean-Claude Juncker, ahead of an informal summit of EU leaders Tuesday.

Rasmussen's liberal Venstre party and Vestager's social liberal Radikale Venstre party — both part of the same liberal ALDE group at the EU level — scored good results in the European Parliament election on Sunday.

Ahead of the EU summit in Brussels, Rasmussen discussed Vestager's candidacy for a European Commission top job with opposition leader Mette Frederiksen of the Social Democrats, which also notched up an election win. The big loser of the Danish vote was Rasmussen's nationalist coalition partner.

If the election result is largely repeated on June 5, when Denmark holds a national vote, that paves the way for an alliance between Rasmussen's liberals and the Social Democrats, who both took a hard stance on migration, said Anne Rasmussen, a political science professor at the University of Copenhagen. One Danish EU official added that Vestager's party might support or even join that coalition, but would not be willing to accept too tough a stance on migration.

"I’m happy … that the liberals in Europe have had a good election. It means that the group in which both Venstre and the Radikale Venstre are members may be decisive," Rasmussen said via video on Facebook Monday.

"Historically, the Social Democrats and the EPP have had the majority — have been able to divide the spoils. That they cannot do this time. They have to listen to us. Hence, there is no doubt that top posts must come our way," he added.

"With that [liberal] cap on my head, it pleases me to see that in Margrethe Vestager we have a liberal candidate for the top post as president of the EU Commission. Right now, she is, no doubt, the best candidate. Moreover, she is Danish. But this will not be settled tomorrow … I have close contact with Mette Frederiksen on this,” Rasmussen said.