Bank of Ireland and AIB Group have agreed to delay issuing repossession orders on homes for 12 months.
The move is part of the Government's bank recapitalisation plan
The banks say delaying repossession proceedings for those in arrears on their mortgages for any longer would be viewed negatively by investors.
The issue of mortgage arrears has become more central in the €7bn recapitalisation talks because of rising unemployment levels.
Negotiations continue this afternoon and any final agreement may be extended as part of a new regulatory code covering mortgage arrears for the entire home loan sector.
The fine detail of the plan is now expected after markets close on Wednesday evening or early Thursday.
The Government had wanted delays in repossession proceedings for two years compared to the current six-month rule.
However, banks raise new funds by issuing bonds against using their mortgage books as security. The banks pay interest on those borrowings.
Carrying mortgage arrears for up to 24 months would make the quality of mortgage-backed securities less attractive to international investors.
It now appears banks are offering not to pursue mortgage arrears for six months and have offered not to repossess homes until 12 months has elapsed.
The compromise has regard to the distressed financial situation arising for many losing their jobs.
Other talking points have centred on executive pay.
Future bad debts
Meanwhile, it appears a firm Government guarantee of AIB and Bank of Ireland's exposure to future bad debts on property development loans is unlikely at this juncture.
The €7bn injection may not be enough to cover future bad debts arising in the property sector, and markets are sensitive to this weakness.
Fine Gael has warned the Government's bank recapitalisation plans may leave taxpayers dangerously exposed to massive bad debts.
In a statement, the party's finance spokesman Richard Bruton said the Government should urgently consider other options, including the creation of 'good banks' with clean balance sheets.
Mr Bruton said Fine Gael has huge concerns that the taxpayer is being asked to put money into existing banks without knowing the full extent of the hole in their balance sheet.
He said there was a real risk that the only result will be to allow the banks to nurse along their dodgy property lending while continuing to starve viable businesses of access to the credit
they so badly need.
The Labour Party's finance spokesperson Joan Burton said this would be the Government's fifth attempt to deal with the banking crisis and it is essential they get this one right.
A spokesperson has said the government hopes to conclude talks with AIB and Bank of Ireland over a recapitalisation deal by Wednesday.
'It is hoped that discussions with the banks will be brought to a conclusion some time tomorrow,' he said.
Taoiseach Brian Cowen will brief Cabinet colleagues later today on progress over the recapitalisation plans.