Theresa May will depend on the unionist party to support her government after her party lost their majority in last week's election.
SDLP Leader Colum Eastwood said: "The Prime Minister will have to do a lot more, however, to convince us that the DUP tail isn't wagging the Tory dog". The UK government, which at that point gave up direct rule over Northern Ireland, was meant to be a neutral arbitrator between the parties.
Mr Adams said they would be pushing Mr Varadkar to raise the prospect of a border poll on Irish reunification within the next five years in discussions with the British government.
It seems with the DUP now wielding more power as a result of their looming deal with the Tories, Scotland might struggle to get the bespoke deal that the SNP hopes for.
Hobbled by a lack of majority after the June 8 election, Prime Minister Theresa May's efforts to strike a coalition with the Democratic Unionist Party (DUP) to shore up her minority government have been hit by a backlash from key parties in Northern Ireland.
Former British PM John Major has also expressed concerns that such an agreement could upend the peace process.
Amid reports that opposition parties will try to bring down Mrs May with a series of targeted amendments to the Queen's Speech, the PM said she was still pushing for an alignment with the DUP.
Here's What The Queen Laid Out In Her Speech To Parliament
In other respects, her speech - which is shaped by the governing party's priorities - was notable for what it left out entirely. The complexity of Brexit has also been underlined as the Government sets out eight bills to deliver Britain's exit from the EU.
The new Taoiseach will sit down with the DUP and Sinn Féin today on the future of the Stormont assembly.
He claimed such a deal could endanger the peace process. "An agreement to restore devolved power-sharing government in Stormont must be reached by the June 29 deadline", he said.
And it wants to ensure a soft, trade-friendly border remains between Northern Ireland and the Republic after Brexit - even though customs and other issues will emerge when the United Kingdom leaves the EU.
He told The Scottish Farmer his party was in a strong position to fight for farmers and fishermen in Brexit talks, which will begin as planned on Monday.
However, Mrs Foster told the BBC's Inside Politics programme that her party wants to explore whether that remains the case because, in the light of Brexit, they argue that European Union (EU) state aid rules should no longer apply.
However, in January, Sinn Fein pulled out of the government over a corruption scandal involving DUP leader Arlene Foster, who is now negotiating with May.
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