Sinn Féin's northern leader Michelle O'Neill said he had still not agreed to release funds for legacy inquests.
Thursday's election ended the unionist majority at Stormont, with Sinn Féin now just one seat behind the DUP.
Talks are being held to restore the power-sharing executive, but parties have just three weeks to reach a deal.
The five main party leaders have held a series of bilateral talks on Tuesday, as well as separate discussions with Mr Brokenshire.
Sinn Féin said it had further discussions with the secretary of state regarding money for inquests into the most controversial killings of the Troubles but that he had come to "no good conclusion".
"Some families have been waiting 45 years and this affects all victims, regardless of the perpetrators," said party leader Gerry Adams.
"They need to get those inquests under way and they have been delayed because the British refuse to give the funds."
The party also met with the DUP and further meetings were planned, said Mr Adams. He added this was an indication that issues were being tackled.
Meanwhile, the head of the Northern Ireland Civil Service, Sir Malcolm McKibbin, said one of the most difficult issues facing the administration was the absence of a budget to cover the financial year from next month.
Sir Malcolm said there was a "small window of opportunity" to allow a new executive to agree a budget and put it to the Assembly.
On Tuesday morning, DUP leader Arlene Foster met her party's freshly elected MLAs (members of the legislative assembly) and said she was "delighted" with their support.
"We have had an excellent group meeting where we had a full and open discussion around the election campaign, the result and, of course, the negotiations that are going on at the moment," she said.
She had previously denied reports that some of her party's MLAs wanted her to step down.
Mrs Foster said her party had won the election, increasing its vote in every constituency, which was a "pretty good basis to continue as leader".
Meanwhile, DUP MP Ian Paisley said the party, and unionism, must try to "make the union as attractive as we can" for voters in the future.
"We have a very attractive case at present and I have been guilty, as a unionist, of presenting it in a rough and combative way over the years when I thought it was required to do that," he told BBC Talkback.
He added that Mrs Foster had his full support.
Earlier, Lord Hain said Prime Minister Theresa May must call a summit to restore the Executive - or direct rule would be inevitable.
The former secretary of state, now a Labour member of the House of Lords, said the London and Dublin governments had "taken their eyes off the ball" and that a summit was now required "to bring all the parties together to thrash out an agreement".
But a senior government source involved in the talks told the BBC Mrs May was being regularly briefed and will have discussions with Taoiseach (Irish Prime Minister) Enda Kenny in Brussels on Thursday.
The DUP went into the election 10 seats ahead of Sinn Féin and, while it remains the largest party with 28 seats, its lead has been cut to just one seat.
Under Northern Ireland's power-sharing agreement, the government must be run by Irish nationalists and unionists together, with the largest party being invited to put forward a candidate for first minister.
Sinn Féin and the DUP now have three weeks to reach a deal and if a government cannot be formed within that time then, under law, another election can be called.
Ultimately, if no power-sharing government is formed, power could return to the UK Parliament at Westminster for the first time in a decade.
Sinn Féin says it broke off its meeting with Secretary of State James Brokenshire because all he did was "waffle, waffle, and more waffle".