Conservative MEPs have been criticised for an alliance with a Swedish anti-immigrant party that has its roots in white supremacism.

The European Conservatives and Reformists (ECR) group, the European parliament bloc dreamed up by David Cameron, agreed on Tuesday to welcome two members of the Sweden Democrats, an anti-immigrant populist party that has been advancing in the polls ahead of Swedish elections in September.

Conservative MEPs, who are members of the ECR, opposed the decision, but other members of the bloc voted to admit the two.

The Sweden Democrats have their links in white supremacist and neo-Nazi fringe groups, but under leader Jimmie Åkesson, the party says it has kicked out extremists.

Welcoming the Sweden Democrats into the bloc, ECR co-chair Ryszard Legutko said: “As the Sweden Democrats move towards becoming a major party of the government in Sweden, we welcome their decision and that of their MEPs to support the ECR group’s agenda for securing meaningful and lasting reform within the EU.”

Other MEPs hit out at the decision. Sophia in ’t Veld, the Dutch vice-president of the European parliament’s Group of the Alliance of Liberals and Democrats for Europe, said the Tories seemed “worrying[ly] comfortable in the company of rightwing extremists, xenophobic and authoritarian outfits that are also openly opposing gender equality, freedom of speech and LGBT rights”.

The Conservative MEPs’ leader, Ashley Fox, said the Tories had opposed admitting the Sweden Democrats to the ECR, but would assist them “on their political journey”.

“Over the past decade the Sweden Democrats have made progress in reforming themselves, expelling any members displaying unacceptable views or behaviour and diversifying their party base,” Fox said. “As a result they are enjoying considerable electoral success.”

“Conservative MEPs acknowledge these efforts but believed the Sweden Democrats needed further time before being admitted to the ECR group,” he said. “However, we respect the decision of our ECR colleagues.”

The Conservatives have attracted criticism over “dubious allies” ever since Cameron, as party leader, decided to quit the centre-right European People’s party to set up a new group, but struggled to make up the required numbers.

Most recently the Tories have been accused of staying silent while the European Union runs its rule-of-law procedure against Poland. Poland’s ruling Law and Justice party is the second-largest party in the ECR bloc, behind the Conservatives.