London mayoral candidate Sadiq Khan says Muslim parents have told him their children have been put off a career in politics after seeing the attacks the he has received during his campaign.

Khan criticised Tory tactics and the alienation it was causing among some British Muslims on Wednesday night at the Muslim News awards, attended by Greg Clark, the communities secretary, and high-profile Muslims from sport, media, business and the armed forces.

He said: “People have approached me here tonight and and even in the last few days and weeks and have said, ‘Look, my son or daughter, my nephew or niece, my younger brother or sister, is thinking about a career in politics, is thinking about public service, is thinking about entering public life. But they are worried. They are worried because if this is what you suffer, we worry that they will suffer’.

“And all I say is this, you know our parents or grandparents who are first generation immigrants, they had it much tougher than we do. When they first came to this country there were signs saying: ‘No blacks, no Irish, no dogs.’ But they made sacrifices, they contributed towards mosques being built, they lobbied parliamentarians to allow halal food, for women to wear what they like, for there to be provision for worship and equal treatment.

“We owe it to them to carry on working hard and make sure we make history.”

He said his campaign had attracted diverse support, adding: “One of the great things of the lives we lead in this great city, this country, is that we don’t simply tolerate each other, we respect each other and we celebrate each other.”

He said of Zac Goldsmith’s rival mayoral campaign: “The next 14 days, they will become more desperate. They’re going to become more negative, and they are going to try to become more divisive. We can’t let them.”

Khan’s comments came after David Cameron stepped up Tory accusations that Khan had links to extremists, accusing him during prime minister’s questions of having shared a platform nine times with a south London imam who Cameron claimed supported Islamic State. The prime minister was met with cries of “racist” from the chamber.

Last week Theresa May, the home secretary, told the Tory spring conference that it was a “worry” Khan had campaigned against the extradition of his Tooting constituent Babar Ahmad, who was detained in the UK without charge and later jailed in the US for helping to support terrorist groups. Goldsmith repeated the claim, but had himself campaigned against the extradition of Ahmad.

Previously in the campaign leaflets specifically targeted at minority ethnic voters warned that a vote for Khan would put their family heirlooms at risk. It backfired when a British-Indian Tory councillor criticised the literature as patronising.

Before this, the word “radical” had been used to describe Khan’s policies in Goldsmith’s leaflets. Khan had said: “Calling someone divisive and radical, be very careful how that’s perceived. You’re playing with fire. When you say that about a candidate of Islamic faith, what are you implying? That will come back and bite you in the bum if you resort to that.”

In an interview responding to the charges, Goldsmith said: “I don’t think there is anything more divisive than playing the race card when it clearly, unambiguously does not apply.”

Goldsmith was also invited to the Muslim News awards but declined because he had other campaign commitments, organisers said.