Negotiations involving the five parties continued at Stormont House after Mr Cameron and Mr Kenny departed yesterday.
The stakes in the talks were raised even higher earlier this month when Chancellor George Osborne said he was willing to accede to a long-standing Stormont demand to devolve corporation tax powers - but only if progress was made in the political negotiations, particularly on budgetary matters.
As well as the latest financial pledge from the UK Government, Mr Cameron and Mr Kenny last night presented a Heads of Agreement document to the five parties involved, proposing potential ways forward on all of the areas of dispute confronting the Executive.
Mr Kenny said he genuinely felt agreement could be reached.
“I have to say the document that was tabled last evening is comprehensive and does address all of the issues that have been involved here for the last period,” he said.
“Politically there is not agreement on the issues that were tabled last evening – that doesn’t mean politicians who are elected and have responsibility devolved to them cannot conclude on a number of these matters,” the Taoiseach added.
At present ministers can draw down money using the Reinvestment and Reform Incentive (RRI) to spend on infrastructure projects in Northern Ireland.
It is understood the terms of the Government’s offer would enable ministers to use RRI money to address other budgetary pressures.
The Government deal does apparently include so-called “new” money to the tune of £10million a year to fund potential new mechanisms to deal with investigations into historic Troubles crimes.