Mr Robinson told UTV's Marc Mallett the fresh threats also extend to the families of the two politicians whose identity he didn't reveal.
The DUP leader was condemning the latest loyalist street violence and campaign of intimidation against political representatives which erupted after Belfast City Council passed a controversial motion to restrict the flying of the Union Flag.
East Belfast Alliance MP Naomi Long received a death threat in the wake of the vote earlier this month.
"Many of our members have been under death threat for a very long period of time so we take it seriously and we empathise with anybody who is under threat," Mr Robinson told UTV.
"We know exactly what it is like when you're under these circumstances yourself."
Mr Robinson didn't say if the latest threats against DUP members were made by republicans or loyalists.
On Monday, a female police officer escaped injury when a petrol bomb was thrown inside a patrol car guarding Ms Long's constituency office in the city.
Mr Robinson said those who are behind the violence are the "enemies of the people".
This is terrorism. This is a despicable act on the part of those involved and they have no right to call themselves loyalists and be attacking the forces of the state.
Alliance leader David Ford has condemned those responsible for the death threats against the DUP members.
Mr Ford said: "I would like to extend the support and solidarity of the Alliance Party to these two DUP members.
"Any threat to a political representative is an attack on democracy. The threats, intimidation and attacks that we have seen against members of my party as well as those of the DUP and Sinn Fein must stop now."
It comes after a meeting of the Assembly Commission to discuss the question of flags at Stormont was cancelled on Tuesday.
The DUP wants to extend the number of designated days for the flying of the Union Flag over Parliament Buildings.
The Alliance Party, Sinn Féin and the SDLP refused to attend the meeting to discuss the proposal.
Mr Robinson told UTV there was "real anger" among unionist politicians at what he called the boycott by parties which he said didn't allow "the democratic process to function."
"Boycotting is not the answer," he said. "Democracy has to function if we are to convince people out there to be calm and to leave it to the political way forward."
An Alliance spokesperson said the party felt it was "impossible to discuss the issue of flags at this time".
"We won't do so until this violence stops. This proposal is destabilising at this critical time and will not do anything to calm tensions on the streets."
Meanwhile, Sinn Féin member of the Assembly Commission Barry McElduff said the decision not to attend was "the right one".
Mr McElduff said: "We are in the middle of a very tense situation arising from the recent Belfast City Council decision on flags.
"The proposal for an Assembly Commission discussion today about extending the number of designated days for the flying of the union flag at Parliament Buildings could only have heightened division rather than promoted mutual respect."
SDLP leader Dr Alasdair McDonnell said: "I formally approached the leader of the DUP yesterday to ask him to reverse his party's decision to refer this matter to today's meeting of the Assembly Commission.
"Because of the community tensions, we do not feel it appropriate to send our representative to the Commission's meeting today."
All unionist representatives indicated their support for a consultation process in relation to the flying of the Union Flag at Parliament Buildings when the matter comes before the Commission for consideration.
Joint unionist statement
UUP leader Mike Nesbitt said the boycott sent "entirely the wrong message".
"Political leadership means doing the difficult things, and at this moment, one of the most difficult challenges is to help stop the violence and address the underlying anger and issues. That can only be achieved through dialogue," he said.
On Tuesday afternoon, Mr Robinson and Mr Nesbitt met with representatives of other unionist parties and independents in the Assembly.
In attendance were TUV leader Jim Allister, UKIP representative David McNarry and Independent MLA David McClarty.
In a joint statement, they said : "The orchestrated failure of the Assembly Commission to meet undermines the democratic process at a time when politics needs to be shown to work.
"Representatives of each of the Unionist parties condemned the ongoing violence resulting in conflict on our streets and reiterated their strong view that any protest must be peaceful.
"The representatives resolved that it was necessary to find a political solution to the issues that were faced and resolved that they would continue to work together to ensure that this was the case in the time ahead."
The Assembly Commission is made up of an MLA from each of the Assembly's five main parties, and is chaired by Willie Hay, the speaker of the house.
An Assembly spokesperson said: "The Assembly Commission meeting, planned for 11 December 2012, did not proceed as a quorum was not achieved. Arrangements will be made to reschedule the meeting."
Unionist politicians said they wanted the meeting to take place no later than Friday.