A prisoner threatened to eat former prime minister Theresa May's corpse, kill Boris Johnson and bomb an MP on behalf of "Jihadis of England".
The 52-year-old also threatened Birmingham Yardley MP Jess Phillips, Birmingham Crown Court heard.
Malik, already in jail for attempted murder, is due for sentence on 18 June.
The HMP Birmingham inmate admitted last month to four counts of making threats to kill and four of malicious communication.
He is said to have a psychopathic sub-type of anti-social personality disorder, the court heard.
Prosecutor Simon Davis said a letter destined for Mrs May - MP for Maidenhead and then prime minister - was received at the Cabinet Office in September 2018.
It stated, he said: "Jihadis of Britain are going to kill the police at the gates. Then I'm going to kill you and then eat your corpse."
The letter and another addressed to her were not delivered to Mrs May personally, the court heard.
It emerged an envelope franked in Birmingham was opened at Ms Cooper's office in May last year, which stated: "You will die the same way as Jo Cox."
The letter also made a rape threat towards Ms Cooper, who had previously been the target of a murder plot by a neo-Nazi terrorist.
A threat to put a bomb in her car made her feel "very scared", Mr Davis said.
'Rantings of disturbed individual'
Within days of Malik being charged with six of the offences in December 2019, two further letters sent by him were intercepted at HMP Birmingham, including one addressed to the prime minister.
The court heard the letter sent to Mr Johnson stated: "I'm going to kill you and your girlfriend. I'm going to blow you both up.
"I'm going to do it by Christmas."
Andrew Jackson, for the defence, said Malik - who is registered blind - described the letters as "the rantings of a disturbed individual who frankly wallows in attention seeking".
Mr Jackson added: "He is a physical wreck - he is a 52-year-old diabetic with heart disease and asthma."
Malik is serving a life sentence imposed in 1999 for the attempted murder of his "cell-mate" at Merseyside's Ashworth high security hospital.
He had previously been convicted of possessing an offensive weapon, indecent assault and assaulting a police officer.