The leading Sinn Féin politician was visited at his home by a senior PSNI officer on Wednesday night to inform him of what has been described as a "real and active" threat on his life, he said.
"Both myself and the PSNI are taking this threat seriously," he explained.
He added: "However there are times when in political leadership staying silent is not an option and I will not be silenced by threats like this. I will defend the peace process from attack from whatever quarter, be it these groups or the loyalist flag protesters over recent months.
"I am very sure of the ground I stand on. I am also very sure that it is the path shared by republicans across this island genuinely interested in building a new agreed Ireland, republicans who put Ireland before ego, criminality and self gain."
It says much about the mentality of those running groups like the one behind the threat that in their warped logic threatening Irish republicans and their families somehow advances the cause of Irish reunification
Mr McGuinness said it may be linked to his condemnation of an attempted dissident mortar bomb attack in Derry, which was foiled by police earlier this week.
Two men were remanded in custody on terrorism charges on Wednesday in connection the planned attack on a police station in the city.
The judge described Seamus McLaughlin, 35, and 37-year-old Gary McDaid as "active and prominent members of a dissident republican grouping".
Meanwhile south Belfast MLA Conall McDevitt revealed on Wednesday that he had received a bullet and a sympathy card in the post.
The SDLP member said he would not be deterred from his work.
Speaking following a Policing Board meeting, PSNI Chief Constable Matt Baggott expressed his outrage at the threats against politicians.
"The vast majority of good people in Northern Ireland have absolutely no place for the intimidation of politicians, people who put themselves in the heart of politics to make lives better," he said.
"There's no place for this whatsoever, and if we are able we will bring the people who have done this before the courts."
We still have a hard core of people who are utterly dedicated to the anger and misery of the past.
PSNI Chief Constable Matt Baggott
The incident comes in the wake of increasing attacks from dissident republicans on both sides of the border.
A new grouping, consisting of members of RAAD (Republican Action Against Drugs) and the Real IRA, calling itself the New IRA - has been behind a number of incidents in the past year including the killing of prison officer David Black in November.
"We've seen a whole array of attacks from groups who are opposed to the peace process over the last few years," the Chief Constable commented.
"From the rocket-propelled grenade we recovered through to mortars, through to explosive form projectiles and of course the targeting of those who are simply here to keep peace."
Mr Baggott said they have seen a variety of threats which continue to change but that the PSNI have invested significant resources to deal with terrorism as well as community policing.
He added: "We've brought many before the courts, prisons are getting full, I hope they eventually decide that the political process is the only way which grievances should be aired."
Sinn Féin MLA Gerry Kelly called for the threat on Mr McGuinness to be withdrawn "immediately".
"Let me make it clear as a republican, if these people who are masquerading as republicans, are threatening Martin McGuinness, they can threaten us all, because we are standing fair and square behind (him)," he said.
"A threat like that is always sinister, these people have tried to kill others, they are capable of killing people, Martin has to take that very seriously.
"But they need to know the message from the people who stand with Martin McGuinness, not just republicans, but nationalists and people in political life, that we will stand against any of these threats."
He said that his party would remain open to talks with those opposed to the current political process.
"Sinn Féin has said clearly that if you want to talk politics, if you want to talk about where we now, if you want to argue your cause, we are more than willing to talk to them and we will always leave that open to talk to them despite the threats.
"They need to desist, the only people they are harming, and the mortars are a perfect example of this, are the people of Derry."