"I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements", Ms O'Neill said in a statement.
The BBC reported that a deal with the DUP was expected to be signed on Wednesday.
It had been suggested the start of negotiations could be delayed by the failure of any party to win a House of Commons majority at last week's General Election.
Sky Sources say that "significant progress" has been made today, while Mrs Foster tweeted to say she hopes to bring a successful conclusion soon.
Scottish Conservative leader Ruth Davidson said the government should put economic growth at the heart of its Brexit strategy, comments placing her in the camp of those advocating a closer trade relationship with the European Union, or "soft" Brexit.
Meanwhile, talks are continuing between the DUP and Conservatives, to secure the support of the DUP's 10 MPs in steering government business, including crucial measures on Brexit, through the Commons.
The first round of talks are likely to focus on the UK's so-called divorce bill, estimated to be as much as €100bn (£88bn), as well as the rights of European Union citizens now living in Britain and United Kingdom nationals living on the continent.
Some observers have maintained that a deal with the DUP risks destabilising Northern Ireland by increasing the influence of pro-British unionists.
But Jeremy Corbyn, leader of Britain's main opposition, said his Labour Party would not support May's Queen's Speech in the lower house of parliament to try to force her out of power through a vote of no confidence. Devolved government at Stormont, site of the Northern Ireland assembly, broke down in January and has yet to restart.
The EU will keep the door open for Britain to return, but only on worse terms than it now has, European Parliament Brexit negotiator Guy Verhofstadt said Wednesday. "It continues and when the deal is done, it will be done", a senior source in the Conservative Party said on Thursday.
The DUP said it was discussing issues to do with Brexit and economic matters in its talks with the Conservatives.
Britain's Prime Minister Theresa May and her husband Phillip arrive at church in Sonning, Britain.
The Times newspaper said finance minister Philip Hammond would push May not to leave the customs union - an arrangement which guarantees tariff-free trade within the bloc but prohibits members from striking third-party trade deals.
Sinn Fein said that it was important there was transparency over any deal between the Conservatives and the DUP, and that compromises over certain policy areas could hinder efforts to form a new Northern Irish executive.
The talks were "productive", May told a news conference in Paris following a meeting with French President Emmanuel Macron.
The Oehler family chose to plan their day around it - celebrating their 21st wedding anniversary by watching Wallenda. In 2011, Nik had held the record after he hung by his teeth 250 feet above Silver Dollar City in Missouri.
Trump has furiously railed against leaks coming out of his administration and the intelligence community since he took office. He has sometimes, without prompting, injected "I'm not under investigation" into conversations with associates and allies.
He also suggested that the Scottish Tories led by Ruth Davidson could also add to the pressure on Mrs May to change course. Brexit will likely be on the agenda at the Paris meeting, after May confirmed she will stick to the negotiating timetable.
Northam, a pediatric neurologist, ran as a pragmatist with the state's Democratic establishment's firm support. But like Perriello, Northam has been unsparing in criticism of Trump, calling him a "narcissistic maniac".
Alex Cuthbert's fine individual try - the wing chipping through and collecting his own kick - was the game's one moment of class. They led 8-3 at half-time with Cuthbert's try and a penalty by Davies, while Sonatane Takulua kicked a penalty for Tonga .
Police said eight of the injured were hospitalized; the other two had minor injuries and were treated at the scene. Eyewitness told Sky News and other British media that the van seemed to have veered and hit people intentionally.
In itially, Shiv Sena had proposed the name of RSS chief Mohan Bhagwat as NDA's presidential nominee. BJP sources said the two leaders agreed to put the recent bitterness behind them and work together.
Republicans and Democrats sat in different parts of the park - fans could state their party preference when buying tickets. They sat next to each other at the game above the first-base dugout, as a show of friendship across the aisle.
The White House recently began referring all questions on Trump and Russian Federation to the lawyer Marc Kasowitz. The Post referred to anonymous sources who had been briefed on requests made by Mueller's investigators.
UK's May confident on power-saving deal
Speaking to reporters after the meeting, Foster, whose party has been locked in talks with the U.K. She has held meetings with key Northern Ireland leaders, including the DUP .
India beat Pakistan 7-1 in Semifinal
Another deflection from Talwinder, this time a much better one, directed into goal when the ball was in the air, made it 3-0. Five automatic berths are available for the men's 2018 Hockey World Cup, which will also take place in Bhubaneswar.
Seoul warns N. Korea not to miss chance to 'develop'
The trial was the first meant to replicate the flight profile of an ICBM that could be deployed by North Korea. US President Donald Trump had also warned that military intervention "was an option under consideration".
Paris: Attacker shot outside Notre Dame cathedral
Notre Dame, which is situated on the banks of the Seine river in the heart of Paris , draws 13 million visitors a year. Tourists panicked by the incident were fleeing the cathedral and surrounding areas for cover, French TV said.