Both the British and Irish governments have said they want to get the talks back on track but neither have suggested when Irish nationalists Sinn Fein and the pro-British Democratic Unionist Party (DUP) should return to the negotiating table.
DUP MPs warned that essential services in Northern Ireland would suffer if Ms Bradley continued to resist calls to restore direct rule.
"In accordance with the Belfast Agreement, this is a devolved matter which should be addressed in the NI Assembly; but the power of the Westminster Parliament to legislate remains unaffected", she stated in a written answer.
"I welcome the Goverment's commitment to allowing a vote on equal marriage in Westminster and would ask that the Secretary of State now set a clear deadline for legislation in either the restored Assembly or United Kingdom parliament because lesbians and gays in Northern Ireland have already been waiting for equality for far too long".
DUP leader Arlene Foster this evening insisted that her party is not contemplating introducing an Irish language act in Northern Ireland.
Both leaders expressed disappointment over the political impasse at Stormont.
The parties still disagree on whether or not a draft agreement was on the table before the talks broke down.
Theresa May to meet DUP and Sinn Féin leaders
He added: "Sadly, equal marriage appears not to have been a sufficient political priority in these talks". The Irish government said there was the basis of a deal and indeed the DUP were briefing that there was the basis of a deal.
"We are trying to defend the Good Friday Agreement from some people who are seeking to undermine it", the Taoiseach said.
"We do need to remain very firmly focused on restoring devolved government and rather than talking up direct rule, we should continue to be focused on talking out the remaining issues that lie between the two parties", he said.
The Taoiseach (prime minister in Irish language) emphasised the Irish government's full commitment to the Good Friday Agreement, and its determination to secure the effective operation of all its institutions, said the statement.
Meanwhile, a number of DUP hardliners have threatened to walk away from any deal that includes same-sex marriage.
In November 2015, a majority of MLAs in the Assembly voted to support equal marriage, but the measure was blocked by the DUP using a Petition of Concern, a voting mechanism created to protect the rights of minorities in Northern Ireland.