Joshua Spencer was jailed for nine weeks at Leeds Magistrates’ Court on Friday and handed a 10-year restraining order.
The 25-year-old Normanton, Pontefract and Castleford constituent wrote in April that he was working to get Ms Cooper "hurt" over her opposition to a no-deal Brexit.
The message, sent to a man he met on a dating website, said: "We should have left no deal on the 29th before the w**** Yvette got her hands on to it and voted to revoke democracy. She will pay. I'm already organising... to hurt her.
"Amazing what crackheads will do for £100. I'm going to get her beat up."
In another message, he said: "If you make peaceful revolution difficult you make a violent one inevitable."
In the Commons today Ms Cooper said the chair of the local association had now written to her “expressing regrets and apologies for what he describes as the grave and unacceptable actions of the member who has since been expelled, and I welcome that letter and that support”.
However she added: “It is a concern to me that there has been thus far no similar condemnation or sense of regret expressed by the national party.
“And the letter to me from the national chair in response to this issue, the strongest it said was ‘intimidating behavior has no place in our politics’.”
She said even though she had raised the case with the Conservative Party, Spencer had still been allowed to attend the election count in December.
And she called on Home Secretary Priti Patel to “condemn these threats in the strongest terms, to look into her party's response, and also to show leadership on this by urging all political parties to come together and draw a new joint code of conduct against intimidation because violent threats must have no place in politics”.
Ms Patel replied: “Let me say this right now on the floor of the house that that is categorically unacceptable, and wrong. There is no place for intimidation at all in public life.
“In terms of the national party response, she can take it from me right now, but I am hugely apologetic for what she has had to [...] put up with, that is simply unacceptable. And that is also something that we should all be mindful of and look into as representatives of major political parties. None of this should be tolerated.”
Ms Patel addressed SNP MP Joanna Cherry who she accused of “chuckling” and added: “I think it's a fact that obviously it's this Government that is trying to deal with these types of issues. You've already heard me speak about dealing with online harms dealing with trolling, calling this unacceptable.”
Ms Cooper also revealed she had not been made aware neighbouring Tory MP Andrea Jenkyns had given a positive character reference for Spencer for the sentencing on Friday.
"I have known Joshua for a number of years. I stand by my decision to have given him a personal reference," the MP for Morley and Outwood said.
"Josh has bipolar and had mental health issues since his father's suicide in 2015 and I was, and remain, concerned about his emotional and mental well-being and wanted to make absolutely sure it was taken into consideration as part of the judicial process.
"I will be seeking assurances that he will get the support he clearly needs as part of his rehabilitation."
But Ms Cooper said: “I'm disappointed too that the neighbouring MP chose to give a very positive character reference for this individual without contacting me first. And I have raised that with her directly.
Ms Patel said Ms Jenkyns’ comments were meant to ensure Spencer got support for his mental health difficulties.
In a statement to the court on Friday Ms Cooper said she has suffered numerous threats in the past but "this case was different and more serious".
"In this case the individual lives in my constituency, has contacted me directly on a regular basis, is an active member of the local Conservative Party and prominent in mainstream local politics in my constituency," she said.
She said her office had provided Spencer with "considerable casework assistance" throughout 2017 and that he went on to bombard her with messages and organise "a hostile event" outside her constituency office.
Ms Cooper has written to the Conservatives asking why Spencer was permitted to attend her election count in December as a Tory representative despite having been summonsed.
"As a result of his political role he will have known my movements for campaign events such as hustings as well as the count. My office had to inform the police about any event he might be present at, including the general election count, as we had no idea whether or what kind of threat he might pose," she said.
"It is only three-and-a-half years since my friend and colleague Jo Cox was killed while in her constituency. Threats of violence cannot be dismissed as banter between friends. Intimidation and violence has no place in our politics."
Spencer was a Conservative candidate for the Wakefield Council elections in May, which was reportedly a month after his arrest.
The activist, of Knottingley, West Yorkshire, admitted a charge of sending an offensive, indecent, obscene or menacing message by a public communication network.
The restraining order demands he does not contact Ms Cooper, including on social media, or go near her constituency office for 10 years, court staff said.