"My name is death to traitors, freedom for Britain," Tommy Mair said when asked his name in the dock.
Mair was not required to enter a plea and the judge did not ask for one. Keith Allen, his attorney, said there was no indication of what plea would be entered.
Deputy Chief Magistrate Emma Arbuthnot ordered Mair to be remanded in custody until his next appearance.
Mair, 52, is accused of killing Cox, a member of Britain's Parliament, in a brazen attack Thursday in her district in northern England. She was stabbed and shot on a Birstall street on a day she was a meeting with her constituents.
One witness near the crime scene Thursday said the gunman shouted "Put Britain first" several times before and after the shooting, the Press Association reported.
Police said he was charged with murder, grievous bodily harm, possession of a firearm with intent to commit an indictable offense and possession of an offensive weapon.
The killing has muted the tone of public discussions over the upcoming British referendum on EU membership, also known as "Brexit," which has focused heavily on immigration
The Brexit campaigning will resume Sunday, both "Stronger In" and "Vote Leave" announced Saturday on social media..
Witnesses to the attack
Prosecutor David Cawthorne, laid out graphic details of the attack during Saturday's court proceedings.
The defendant approached Cox and repeatedly stabbed her with a large knife, causing her to fall to the floor, Cawthorne said, citing witness accounts.
Then, the suspect shot her three times as she lay on the ground, Cawthorne said.
Mair repeatedly stabbed Cox as she struggled and fought for life. During the attack, Mair was heard to say words to the effect of, "Britain first, keep Britain independent, Britain always comes first, this is for Britain."
Mair also stabbed 77-year-old Bernard Carter-Kenny, Cawthorne said. Kenny had stopped his car to drop off his wife at Birstall Library when he recognized Cox, who was on her way to meet constituents at the library after meeting with people at a seniors home.
The knife-wielding man attacked Cox as she left her vehicle, Cawthorne said.
Kenny scrambled out of his vehicle to help Cox. The attacker drove a large knife into Kenny's abdomen and he then struggled to get to a local café for help, the prosecutor said.
Kenny suffered a serious injury and is in stable condition at a hospital, Cawthorne said.
Why was Cox targeted?
Cox, a 41-year-old mother of two, was an avid campaigner for the rights of refugees
. Her death comes a week before the so-called Brexit, a crucial referendum on whether Britain should stay in the European Union. She was an open supporter of remaining in the bloc.
Last week, the MP wrote a passionate defense
of remaining in the EU in the context of UK immigration policy. Writing in a local newspaper, The Yorkshire Post, she acknowledged the concerns some of her constituents have over migration.
Cox wrote that "concern" about immigration doesn't mean people are "racist or xenophobic," and that worries over jobs, education and other factors perceived to be worsened by immigration are legitimate.
However, she dismantled arguments put forward by the "Leave" campaign, arguing that leaving the EU would not significantly alter the number of migrants coming into the country, and that alternate immigration proposals, such as a "point system" similar to Australia's, would not necessarily tamp down numbers.
She suggested measures for ensuring that benefits for migrants are more closely controlled and tax revenues from their income go to the communities impacted by net migration.
She ends the opinion piece by repeating the often-made point that "the overall benefits of EU membership are huge.
"While the leave camp are trying to distract voters, their economic case has been completely demolished by everyone from the President of the United States to small and medium businesses in Yorkshire."
She ended by saying, "Please don't fall for the spin prior to June 23 that the only way to deal with concerns about immigration is by voting to leave -- that simply is not the case."
Police explore Mair's ties to white supremacist group
Police said in a statement that the incident "appears to be an isolated, but targeted attack."
Authorities are also investigating how the suspect got a firearm and are looking into his mental health.
Mair may have had an interest in white supremacist groups, according to the U.S.-based Southern Poverty Law Center, which published
what it says are documents showing his history of purchasing material from the National Alliance white supremacist organization.
The center released copies of receipts and a 2013 subscription to the National Alliance's publication National Vanguard as well as receipts from 1999 showing purchases for the neo-Nazi book "Ich Kampfe," the "Improvised Munitions Handbook" and other books.
Mair also subscribed to a pro-apartheid group's magazine in the 1980s.
"A Mr. Thomas A. Mair from Batley in Yorkshire subscribed to our magazine S.A. Patriot when we were still published in South Africa itself," magazine editor A.D. Harvey told CNN, adding the publication had "no further contact with him" after brief correspondence in the mid-1980s.
"We were of course appalled and sickened to learn of the murder yesterday, of Ms. Jo Cox," Harvey said.
Neighbors describe Mair as a loner and a "quiet" man who tended his garden and showed no particular political leanings. He kept to himself most of the time, but he engaged in conversations with neighbors when they spoke to him, they said.
Mair lived in the house for a long time, one neighbor said. She said she didn't believe he had a regular job and saw him around at odd hours.
A half-brother, Duane St Louis, told ITV News
he never saw any sign that Mair had an interest in knives or guns, and said he had "never been in trouble" and "wouldn't hurt a fly."
In a nation with tightly controlled gun laws and few homicides linked to weapons, Cox's attack was especially jarring.
Crowds gathered for vigils in Birstall
and in London's Parliament Square to pay tribute to Cox.
Friday afternoon, Prime Minister David Cameron and his political rival, opposition Labour leader Jeremy Corbyn, united to pay respects to Cox, attending a memorial service in the heart of Birstall.
There was an outpouring of emotion and support from family and friends as they gathered to pay their respects to Cox on Saturday.
"We have to continue the strength and solidarity in the days, months and years to come as part of Jo's legacy," Cox's sister Kim Leadbeater told media and onlookers at the Birstall memorial. "And to focus on, as Jo would say, 'that which unites us and not which divides us.'"