McGuinness angered by threats to Foster and article on his health
Martin McGuinness has led the political condemnation of death threats against outgoing First Minister Arlene Foster.
The Sinn Fein MLA lambasted the threats as the work of "cowards".
Mr McGuinness said the reported threats on social media - including one claiming the DUP leader should be beheaded - were "shameful and totally unacceptable".
In his first remarks on Twitter for several days, Mrs Foster's former power-sharing partner - who resigned on Monday - said he unreservedly condemned the menacing of the DUP leader.
"The reported threats to Arlene Foster are shameful and totally unacceptable," Mr McGuinness wrote. "I unreservedly condemn those responsible for the cowards they are."
Mr McGuinness was warned by police more than a year ago that dissident republicans had threatened to kill him in a rocket attack.
Ulster Unionist leader Mike Nesbitt also said there was "no place" for such online abuse.
He added: "No place for it. Totally unacceptable. I condemn unequivocally."
SDLP leader Colm Eastwood commented: "No politician should have to endure any level of threat for carrying out their role as an elected representative.
"I want to condemn unequivocally the threat against Arlene Foster. My thoughts are with her and her family."
Alliance leader Naomi Long also said the online abuse and trolling of Mrs Foster was "completely unacceptable", adding there was "no excuse for bullying".
In an interview with the Impartial Reporter newspaper, Mrs Foster said the PSNI was investigating several sinister threats against her, including "one that wanted me beheaded".
A PSNI statement said: "We do not discuss the security of individuals. However, if we receive information that a person's life may be at risk we will inform them accordingly.
"We never ignore anything which may put an individual at risk. No inference should be drawn from this."
Meanwhile, Mr McGuinness appealed for privacy and hit out at media reports detailing his illness.
The former Deputy First Minister has suffered ill health for a number of weeks.
Sinn Fein said the veteran politician was receiving the best of care and that he had been heavily involved in talks over the current political crisis engulfing the political institutions.
On Thursday, The Irish Times published an article detailing Mr McGuinness's condition.
Responding, the Foyle MLA said he was "very disappointed" that the article had been published.
"I have always considered my health a private matter," said a statement reported by The Journal.
"The media in the main, has respected my privacy. I am thankful to them for that.
"I am very disappointed that The Irish Times are not respecting that privacy and believe that this will cause my family distress."
Mr McGuinness tendered his resignation on Monday over Mrs Foster's refusal to step aside as First Minister to allow for an investigation into the Renewable Heating Incentive scandal.
Questions were raised about his health at the Press conference.
And later Sinn fein president Gerry Adams admitted his appearance may have shocked people.
However, he said his health had not influenced his decision to resign, and added he had been deeply involved in his party's response to the 'cash for ash' affair.
Mr Adams also thanked those who had wished Mr McGuinness well.