Bradley remained resolute on the topic of devolution, saying: "We want local politicians making decisions on local matters to be accountable to a local assembly".
Both leaders expressed disappointment over the political impasse at Stormont.
The Dup says it can not agree to a dedicated Irish language act, while Sinn Fein says that a return to direct rule from Westminster is not a possibility.
Last week, a group of LGBTQ teenagers delivered a petition of more than 14,000 signatures to the Secretary of State's office calling for the United Kingdom government to deliver marriage equality legislation at Westminster.
"If the Government will not commit to doing that in a reasonable timeframe, then I am prepared to take forward a Private Members' Bill or propose amendments to an appropriate Government Bill to extend equal marriage to Northern Ireland".
"Frontline staff have been living hand to mouth for too long".
"We will continue to explore with the parties whether the basis for a political agreement still exists".
The parties still disagree on whether or not a draft agreement was on the table before the talks broke down.
Sinn Féin and the DUP - Northern Ireland's two main parties - had been in negotiations to end a 13-month stalemate at Stormont.
"We are calling on the UK Government to introduce legislation at the earliest opportunity to bring Northern Ireland's laws on marriage equality into line with the rest of the UK". 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.
"That is not good enough and we demand change".
"The Government can fix this problem and be assured of overwhelming support across both Houses of Parliament".
"Michelle and I will be telling the Taoiseach and the British Prime Minister it is the responsibility of the two governments to implement the agreements on legacy and an Irish Language Act and to provide for marriage equality".
A DUP spokesperson told the Belfast News Letter last week: "The DUP has a mandated policy to defend the current definition of 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.More news: Chelsea boss Conte: We need ideal game against Barcelona
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