Mrs Cox’s sister Kim Leadbeater and her parents Jean and Gordon said in a statement that they were “deeply saddened and shaken by the events in London”.
And they said “immeasurable kindness” shown to them in the nine months since the murder of the Batley and Spen MP had helped them cope with the “horrific” event.
Separately, Mrs Cox’s widower Brendan said the perpetrator of the Westminster attack “is no more representative of British Muslims than the man who killed Jo is representative of people from Yorkshire”.
The Leadbeater family said in a statement: “We would like to send our heartfelt sympathy and sincere condolences to the families of those who lost their lives, including Pc Keith Palmer.
“We would also like to extend our love and support to the surviving victims, their families and anybody who witnessed or who has been affected by this horrendous attack.
“People feel helpless when such horrific things happen, but one thing which has enabled our family to get through the last nine months has been the immeasurable kindness that we have been shown by the vast majority of people in this country and beyond - family, friends and many, many complete strangers.
“Whilst the police conduct their investigation, we would therefore encourage people to reach out and support those who were involved in the attack yesterday, in whatever way they can. Whilst they may feel it, let them know that they are not alone.
“When we are faced with such acute pain and suffering it is difficult not to lose hope, but we must remember that the goodness of humanity will prevail and we must come together and counteract hatred, in whatever form, with love and support for our fellow human beings.”
Mr Cox, whose wife was stabbed and shot by a right-wing extremist outside her constituency office in Birstall, West Yorkshire, last June, today urged everyone to focus on those who had died and the families “waking up with their hearts torn out”, rather than terrorists.
He said: “Anybody who uses this attack to justify their own vilification of Muslims as a group does the work of the terrorists, turning community against community when what we need is unity.
“The person who perpetrated this attack is no more representative of British Muslims than the man who killed Jo is representative of people from Yorkshire.
“The terrorists’ strategy is to make us all - whether we’re Muslims or Christians, Jewish or Hindu, atheist or agnostic - believe the same thing: that we can’t all live together, that we can never live alongside each other. As British people we know that’s just not true.”
Mr Cox said earlier on Twitter that the “name I will remember” from the Westminster atrocity is Pc Keith Palmer - not the knifeman who killed him.
He said in his statement issued on Thursday: “First and foremost, we must remember this morning that families are waking up with their hearts torn out. Kids without parents, wives without husbands.
“I believe strongly that we should deny terrorists the notoriety they seek and keep the focus on the people we have lost and their courage, which is the story that really matters.
“Looking forward, we must react to this attack in a way that defeats the terrorists’ objectives. The point of terrorism is not to win militarily but to strike fear into our hearts and to divide our communities. We have to show that neither will work, that we are resolute and we remain united.”
Neo-Nazi Thomas Mair, from Birstall, received a life sentence with a whole life tariff for the assassination of Batley and Spen Labour MP Mrs Cox days before the EU referendum last summer.