Foreign Affairs Minister Simon Coveney and new Northern Ireland Secretary Karen Bradley will meet again next week in the hope of making progress on the powersharing deadlock.
Mr Coveney, who flew into London from a visit to the Middle East to meet the newly appointed Northern Ireland Secretary, said the talks had been "very good" and he expected they were "going to work very well together".
The Tánaiste said there remained "significant challenges" but both governments wanted to find a way to resolve the stand-off.
He said: "Everybody knows that there are time constraints in terms of the work that we need to do but also I think everybody agrees that we want devolved government again in Northern Ireland."
The meeting came after a week where political relations in Northern Ireland were further strained, this time by controversies around the 1976 Kingsmill massacre in south Armagh.
Mr Coveney attacked the "really, really stupid and insensitive" actions of Sinn Féin MP Barry McElduff, who posted a social media video of him with a Kingsmill branded loaf on his head on the anniversary of an atrocity that saw republican paramilitaries shoot dead 10 Protestant workmen.
Mr McElduff, who apologised and insisted the video was not a reference to the massacre, was suspended by Sinn Féin for three months.
Unionists reacted angrily, both to the post and the extent of Sinn Féin's punishment, and the incident appeared to further reduce the already bleak prospects of a deal to restore powersharing.
The situation was exacerbated on Wednesday when a number of unionist politicians retweeted a graphic satirical cartoon that portrayed the Mr McElduff controversy by depicting the aftermath of the Kingsmill outrage, with blood running from a bullet-riddled van.
The incidents prompted the sole survivor of the Kingsmill shootings, Alan Black, to implore politicians on all sides to stop trying to "poke each other's eye out" and instead help the victims.
However, a week of political rancour and animosity appeared to end on a more optimistic note when two senior DUP and Sinn Féin members engaged in more conciliatory exchanges on BBC NI's The View on Thursday night.
In a forthright condemnation of the Kingsmill outrage, Sinn Féin's John O'Dowd, who lost three family members at the hands of loyalist paramilitaries the day before Kingsmill, said he was "ashamed" by the sectarian attack.
The DUP's Edwin Poots welcomed the remarks and said his party was determined to see devolution returned.
Mr Coveney said: "I think the unfortunate things that have happened in relation to Kingsmill this week and the absolutely understandable upset of families because of a really, really stupid and insensitive occurrence is a reminder of just how important legacy and reconciliation is.
"So, that's why I hope people will get some encouragement from the tone of the interaction between Edwin Poots and John O'Dowd last night, which I hope is the tone we can continue in."
Speaking after the meeting, Mr Coveney also told reporters that he did not believe there was any ambiguity in the agreement reached in December on the Northern Ireland border during Brexit negotiations.
He said: "I don't think there is any ambiguity in the context of an all-Ireland economy and the need to protect north-south cooperation in the context of the Good Friday Agreement."
Meeting Mr Coveney inside the NIO offices, Mrs Bradley said: "We have a shared objective - restoring devolved government to Northern Ireland as soon as possible."
She noted that she had now had discussions with all the main parties at Stormont and Mr Coveney.
"I look forward to reflecting on those conversations over the weekend to decide the way forward," she added.