The UK has a "legal obligation" to let some prisoners vote under a 2005 European ruling, a minister has said.
Minister Mark Harper said the coalition accepted a need to change the law but had not yet decided which inmates it would affect.
Five years ago the European Court of Human Rights (ECHR) ruled the UK's long-standing voting ban was unlawful.
Ministers have been advised that continuing to resist the ruling would lead to costly compensation payouts.
Mr Harper told the Commons: "I think every member in the House is exasperated about this but we have no choice about complying with the law.
"The fact that the previous government failed to do what it knew was necessary for five years has left our country in a much worse position, both in terms of having to pay damages potentially, and case law has moved on.
"The only thing worse than giving prisoners the vote would be giving them the vote and having to pay them damages."
The ECHR ruling in 2005 considered a "blanket ban" to be discriminatory in a case brought by convicted killer John Hirst, of Hull.
He told BBC Radio 4's Today programme prisoners must have a legitimate channel through which to air their grievances.
"In this system where you've got a democracy, people can put pressure and lobby in parliament for changes in the law and improved conditions, but you can't do that if you haven't got the vote," he said.
"All prisoners can do is riot, if they've got a complaint, so you've got to give them this legitimate channel."
But think tank Civitas said making MPs more responsive to criminals was not what a law-abiding society needed.
Director David Green said the government had been forced into the decision by the ECHR and added: "It is another example of judges acting as if they were politicians. It is judicial empire-building."
Prime Minister David Cameron is said to have reluctantly accepted there is no way of keeping the 140-year-old ban on sentenced prisoners voting in general elections, according to BBC political correspondent Reeta Chakrabarti.
But our correspondent said the PM would resist allowing the vote to those prisoners who had committed the most serious offences, such as serial killers and child murderers.
Under the ECHR ruling each country can decide which offences should carry restrictions to voting rights.
It is also thought judges may be given responsibility for deciding which criminals should be allowed to vote when sentencing.
Lord Falconer, a former Labour justice secretary, said he disagreed with the ECHR's ruling, but accepted the government ultimately had to comply with it.
He said individual countries should be able to impose a voting ban on convicted prisoners, and rejected the ECHR's verdict that it contravened the European Convention on Human Rights.
Suggestions that the UK could simply pull out of the convention to get around the problem were "incredibly disproportionate and wrong", he told Today.
The Scottish government, meanwhile, has restated its opposition to giving prisoners the right to vote.
But a spokesman for First Minister Alex Salmond said although justice was devolved to Scotland, the decision on voting eligibility and compensation claims was a "reserved matter" for the UK government and not for Holyrood.
Prisoners on remand awaiting trial, fine defaulters and people jailed for contempt of court are already permitted to vote but more than 70,000 prisoners currently serving sentences in UK jails are prevented.
Inmates were originally denied the right to vote under the 1870 Forfeiture Act and the ban was retained in the Representation of the People Act of 1983.
The former Labour administration has undertaken a series of consultations on the voting rights of prisoners but has not legislated on the issue.
In June the Council of Europe, an inter-governmental organisation that oversees and enforces rulings made by the ECHR, urged the coalition to act.
Juliet Lyon, director of the Prison Reform Trust, told the BBC many prison governors believe voting is an important part of resettlement and prison is about rehabilitation as well as punishment.
Frances Crook, director of the Howard League for Penal Reform, said the right to vote was a good means of engaging individuals with the responsibilities of citizenship ahead of a safe return to the community.