Mr Robinson (66), who suffered a heart attack in May, took ill on Saturday night and was admitted to the Royal Victoria Hospital in Belfast.
It will report back next month and conclusions be used to inform the cross party talks process.
A DUP spokesman said Mr Robinson was admitted to hospital as a “precautionary measure” after suffering an adverse reaction to medication.
Mr Robinson added: “We need to know exactly whether they are collecting intelligence, whether there is any weaponry being brought in, whether there is a recruiting going on (and) what activities are they involved in”.
Deputy First Minister Martin McGuinness tweeted: “Concerned that Peter Robinson admitted to hospital but pleased he is comfortable and doing well”.
Ulster Unionist Party leader Mike Nesbitt also wished Mr Robinson a speedy recovery.
Today’s talks will be hosted by Northern Ireland Secretary Theresa Villiers and Irish Minister for Foreign Affairs Charlie Flanagan.
All five main political parties represented in the Northern Ireland assembly will attend the talks, which are created to prevent power-sharing and devolution from collapse.
At the time, Robinson blamed his illness on an unhealthy lifestyle rather than the stress of his job.
Peter Robinson, who said he felt “better already”, said outside Parliament Buildings: “We’re determined to apply ourselves and we’re wanting to see a positive outcome”.
She said: “I recognise the scale of the task ahead”. “You can’t have a functioning government without a workable budget and you can’t have a functioning government if relationships between partners have broken down completely over this paramilitary problem”, she said.
On Friday, Northern Ireland Secretary Theresa Villiers’ proposal for an independent examination of the role, structures and objective of paramilitaries was accepted by the DUP and UUP who committed to being at the negotiating table.
“We’re delighted that the issue was diagnosed and he was able to leave hospital”. But Northern Ireland’s political leaders have achieved great things over the past 20 years (by) working together.
On the agenda will be the full implementation of the Stormont House Agreement which aims to tackle legacy issues relating to the Troubles, the budget, and controversial welfare reforms.
“There is a huge responsibility on all parties, including ourselves, and also the two governments to be creative and deploy a spirit of generosity in the course of these discussions”.
The political crisis at Stormont erupted last month after George Hamilton, the chief constable of the Police Service of Northern Ireland (PSNI) said the IRA still existed and that some of its members had murdered ex-republican prisoner Kevin McGuigan.