Thomas Mair, 53, had declined to enter a plea at a pre-trial hearing in October, so a judge had recorded a plea of not guilty on his behalf.
Labour MP Cox, 41, was shot three times and repeatedly stabbed on the street in the town of Birstall, part of her electoral district in northern England, a week before Britain voted to leave the EU in June.
Defence lawyer Simon Russell Flint told jurors at London's Old Bailey court: "We call no evidence for Mr Mair."
Judge Alan Wilkie said the jury could draw their own conclusions if he declined to offer evidence. Russell Flint said his client was aware of that.
Earlier the jury was told that when Mair appeared at London's Westminster Magistrates Court after being charged he had given his name as "death to traitors, freedom for Britain".
On Monday, the court heard police searching Mair's house had found Nazi materials including books and an eagle ornament bearing a swastika.
Witnesses have said Cox suffered a ferocious attack when she arrived at the Birstall library to give an advice session to local residents, and that when apprehended by police Mair had said "It's me" and described himself as a political activist.
Jurors heard Cox's assailant had shouted something like "Keep Britain independent" and "Britain first" during the attack.
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