The chairman of the Conservatives, James Cleverly, has apologised after a string of allegations of Islamophobia and racism by the party’s parliamentary candidates.

The Guardian revealed on Friday that at least four ministers had gone on election campaigning trips to endorse Tory candidates who had, among other things, argued that Muslims had divided loyalties and blamed immigrants for bringing HIV to Britain.

Speaking to BBC Radio 5 live’s Pienaar’s Politics programme on Sunday morning, Cleverly was asked whether he was sorry for cases of Islamophobia involving candidates. “Well, course, I’m sorry. And I’m sorry when, you know, people do or say things that are wrong,” he said. “But I am, I am confident that my party has a robust mechanism for dealing with it.

“We investigate this. It’s done independently. We have independent people looking at this and they come to adjudications and where people have had to be either sanctioned or expelled from the party, that has happened.”

Despite repeated reassurances they take allegations of Islamophobia seriously, government ministers have continued to endorse candidates who have been accused of making offensive statements.

This week, the business secretary, Andrea Leadsom, paid a visit to the Conservative candidate in Lincoln, Karl McCartney, who had previously retweeted posts from Tommy Robinson. The health secretary, Matt Hancock, has visited Anthony Browne, the Tory candidate in South Cambridgeshire, who previously wrote that the policy of “mass migration” was “letting in too many germs”.

Cleverly said the party would launch an inquiry into Islamophobia and other types of racism within its ranks this year, after the election, and that preparatory work had already started.

“It will specifically look into Islamophobia in my party. And it will, by definition, also have to look at other stuff as well, because you can’t always unpick this,” he said.

“But we are and absolutely have always been clear on this. We recognise that in mass-membership organisations that will always be people that say and do things which are completely inappropriate.”

He added that Boris Johnson had apologised for likening Muslim women who wore the face veil to “bank robbers” and “letterboxes”, claiming that the prime minister had actually been making a point about the importance of personal freedoms.

“The point he was making was that actually in a healthy liberal democracy like we have here in the UK, just because someone has, you know, a personal discomfort with that does not mean that [form of dress] it should be banned,” said Cleverly. “And that is a defence of our liberal democracy.”

The Conservative party confirmed on Saturday that it was investigating three parliamentary candidates over antisemitism. Among the allegations is that one shared a video with an image implying that the billionaire George Soros, who is Jewish, controls the EU, while another asked whether a Jewish journalist was more loyal to Israel than to Britain.

Cleverly’s comments came as Labour’s John McDonnell admitted he was concerned that the antisemitism row in his own party risked damaging their electoral chances. The shadow chancellor repeated his apology to the Jewish community for what he called Labour’s failure to be “quick enough or ruthless enough” in dealing with complaints of antisemitism.

Documents from Labour’s disciplinary department, which were leaked to the Sunday Times (£), included a recording of an official complaining that more than 130 cases were outstanding even though the majority were reported to the party 18 months ago and one had been on the books for more than three years.