A member of the UK cabinet revealed he received a death threat after MPs backed airstrikes against Islamic State (IS) in Syria.
Scottish Secretary David Mundell said police had advised him of a "credible" threat in the wake of a Commons vote in favour of the action in December 2015.
He said, however, that MP Jo Cox would not have wanted politicians to "pull up the shutter" and become less accessible to the public.
Read more: Parliament to be recalled as Jeremy Corbyn calls Jo Cox's death 'an attack on democracy'
Mrs Cox was shot and stabbed to death in the street outside her constituency advice surgery in Birstall, West Yorkshire.
Mr Mundell said: "I didn't make it public at the time, but immediately after the Syria vote I received what police regarded as a credible death threat.
"It's very concerning, not just for yourself but for your family, your staff in particular.
"The police do offer very good guidance and support in relation to how to carry out your duties in the safest possible way.
"But, ultimately, accessibility is at the heart of politics and you can't let those people who want to disrupt our political system win by refusing to be accessible to the public.
"I know Jo Cox would not have wanted us to pull the shutter up as a response to yesterday's dreadful events."
He criticised the "vilification" politicians are subjected to, saying "we've come to accept abuse and name-calling as a matter of course".
Read more: Conservatives will not contest Batley and Spen by-election after death of Jo Cox
He continued: "When people hear about Jo, they understand that she is the exact opposite of the stereotype, somebody who wasn't in it for themselves, somebody who took huge personal sacrifices, having a young family, having to come to London, because she wanted to do better for her community and the wider world."
Mr Mundell made the comments after the British-Irish Council, which is made up of representatives of all the governments and devolved administrations in the British Isles, met in Glagsow.
The talks were chaired by Scottish First Minister Nicola Sturgeon and began with a minute's silence as a mark of respect for Mrs Cox.
"It's fair to say yesterday's tragic events hung very heavily over all our deliberations this morning," Ms Sturgeon said.
"It's important I begin by expressing on behalf of all the member administrations our horror at the brutal and senseless murder of a young, brilliant, dedicated, compassionate Member of Parliament as she went about her constituency duties.
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"We all want to convey our heartfelt sympathies to Jo's husband, to her two young children, her wider family and everyone who loved her."
She continued: "As politicians, we all value and are deeply committed to the openness and accessibility of elected representatives to the people we serve. It is, in very many ways, the hallmark of our democracy.
"So, events like yesterday's, although thankfully very rare, hit all of us as politicians very hard.
"I think I speak on behalf of all of us when I say that we are all determined, inspired by Jo Cox, to rededicate ourselves to the notion of politics and public services as a force for good."
The standards at Scottish Government buildings, the Scottish Parliament and Palace of Holyroodhouse in Edinburgh were lowered in tribute to Mrs Cox.
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