Senior Conservatives have suggested that the European commission president, Jean-Claude Juncker, should be investigated over claims he encouraged tax avoidance while running the government of Luxembourg.

Iain Duncan Smith, the work and pensions secretary, said it was time for European commissioners to show they had “no fear of investigating their own”. Grant Shapps, the Conservative party chairman, said it was “absolutely right that it is properly investigated”.

The comments mark an escalation of pressure from members of the UK government on Juncker, whose appointment to the top job in Brussels was fiercely opposed by the UK prime minister, David Cameron.

The former Luxembourg prime minister and finance minister has denied any wrongdoing. But at the G20 summit in Australia he faced pressure over allegations that he encouraged companies to minimise their tax bills by locating in Luxembourg.

Duncan Smith said on BBC Radio 5 Live’s Pienaar’s Politics programme: “This is a real moment for the European Union, for the commission, to show that it has the capacity and the determination to investigate its own and so if there is an issue, if there is some serious issue about a conflict and at one time one thing is being said and at another thing is being done, then these things need to be investigated and made public. And as soon as they’re made public decisions have to be taken.

“The trouble for the European Union historically has been that it circles the wagons around the people that are having the finger pointed at them and refuses to let any kind of change takes place.”

When pressed on whether he was referring specifically to Juncker, Duncan Smith said: “Yes. I would say the same by the way if it were Britain. You need to make sure when you’re saying one thing and doing one thing that you don’t then say and do another at the same time, so there has to be an absolute clear purpose and at the same time a determination of the European commission to make sure this whole issue is not brushed under the carpet but is transparent, open and investigated and then decisions can be taken one way or another.”

On the same programme, Shapps said he hoped the matter would be investigated, and added: “Either way the important thing is to hold Europe to account and to do that you’ve got to have a credible in-out referendum so you can have these negotiations about all of this stuff.”

Pat McFadden, the opposition Labour Europe spokesman, said there was little chance that Juncker would resign at this stage, but “if more comes out on this then really serious questions will have to be asked about his position”.

At a media briefing on Saturday, Juncker ignored questions about whether he should resign and said he supported only fair tax competition between countries.

Juncker is charged with leading the EU campaign to convince other countries to exchange tax information automatically between jurisdictions but he has brushed aside suggestions he might not be a credible figure to lead such a project.

“Due to very divergent national tax levels in accordance with the law we can get a situation [in which] the result is a very low taxation of companies,” he told the conference at the G20 summit in Sydney.

“This has to be avoided. Things of that kind happen because of the discrepancy between national tax legislation. What we are intending now is not fully-fledged tax harmonisation in each and every detail but eliminating from our tax legislations the open gates [for tax avoidance]. I’m in favour of tax competition but I’m also in favour of fair tax competition.

“We would like the 20 countries to join the efforts of the Europeans to have greater transparency in the tax field and we will do everything possible to support the base erosion and profit-shifting action plan.”