"We will not stand for hate crime or these kinds of attacks, they must be stamped out."
Mr Cameron moved to reassure European citizens living in the UK and Britons living abroad that there will be "no immediate changes in their circumstances".
He highlighted that there will be no "initial change" to the way in which people in the UK travel or to the way goods move and services are sold.
He also suggested the country is "well placed" to face any economic challenges arising as a result of Brexit.
David Cameron addressed MPs for the first time since the Brexit vote
PA
He said: "It's clear that markets are volatile. There are some companies considering their investments and we know this is going to be far from plain sailing.
"However, we should take confidence from the fact that Britain is ready to confront what the future holds for us from a position of strength.
"As a result of our long-term plan we have today one of the strongest major advanced economies in the world.
"We are well placed to face the challenges ahead.
"We have low stable inflation, the employment rate remains the highest it's ever been, the budget deficit is down from 11% of national income forecast to be below 3% this year."
The Prime Minister also insisted that the financial system is "substantially more resilient than it was six years ago".
Mr Cameron also set out how the EU unit in Whitehall, set up to work out the complexities of the UK's divorce from Brussels, will work.
He said: "Clearly this will be the most complex and most important task that the British Civil Service has undertaken in decades, so the new unit will sit at the heart of Government and be led and staffed by the best and brightest from across our Civil Service."
The unit will be responsible for ensuring that the person who takes over as prime minister is given the "best possible advice from the moment of their arrival".
Mr Cameron insisted the UK's devolved administrations will be "fully involved" as the Government works on the negotiations.
