Theresa Villiers and Charlie Flanagan both attended a meeting to review the implementation of the Fresh Start deal negotiated in November last year.
Both the British and Irish governments said the momentum created by the agreement must be maintained.
Mrs Foster became Northern Ireland's first female first minister on Monday.
The Democratic Unionist Party leader took over from Peter Robinson, who confirmed his resignation in the Northern Ireland Assembly.
Mrs Foster is the youngest person to hold the most senior post in Northern Ireland politics.
Speaking after Thursday's meeting, Mrs Foster said she was "absolutely delighted" by how the Fresh Start agreement had been implemented.
"Good progress has been made and we'll continue to make that progress," she added.
She said the legacy of Northern Ireland's Troubles had been discussed and that there was a need to talk to victims' groups.
Earlier, Northern Ireland Secretary Theresa Villiers said "significant progress" had been made since the Fresh Start agreement was made, but "substantial challenges" remained.
She added: "Work continues with victims' representatives and others on finding a way forward to address the legacy of Northern Ireland's past."

On Radio 4's Today programme, Mr Dyson called for an easing of immigration laws to keep more overseas engineers.
He also said he would vote to leave the EU to avoid being "dominated and bullied by the Germans".
The firm has committed £1bn to 100 new products over four years.
"Export is vital for Britain to create wealth," said founder and chairman James Dyson. "In order to export you have to have high technology products that are better than those produced elsewhere in the world."
To boost UK research and development, engineers who come to study in UK universities should be encouraged to work in the UK after their course has finished, Mr Dyson said.
"One important thing we should do is to keep those engineers in Britain. A lot of them come from overseas, in fact, 90% of researchers at British universities come from overseas, and we must encourage them to stay here."
"I would change our immigration laws to allow the right sort of people to stay here," he said.
In addition, Mr Dyson said he didn't particularly want to stay in the EU.
"I think it's a European Union dominated by Germany, and in our particular field we have these very large German companies who dominate standards setting and energy reduction committees, and so we get the old guard and old technology supported and not new technology.
"I want to keep EFTA - European free trade - and free movement of peoples, but I don't see that we need to be dominated and bullied by the Germans."
Dyson's £1bn investment plan represents a significant increase in R&D spending at the company, which first made a name for itself selling bagless vacuum cleaners.
Since then it has produced fans, heaters and powerful hand dryers for public toilets.
Dyson also announced an extra £45m investment in research at UK universities.
The company has already made a commitment to spend £5m on a robotics lab at Imperial College London, but there was no indication as to which other institutions would receive funding.
In January, the firm said it would invest £250m to expand its Malmesbury research and development campus, and create 3,000 jobs.
Reacting to Dyson's announcement, Prime Minister David Cameron said it signalled that the company was "looking to the future", and that its investment would "help to cement its leading role on the global stage".
Dyson also announced an investment of £200m for manufacturing expansion in South East Asia.
A proportion of the investment will go to its West Park motor factory in Singapore.
Dyson faced criticism for a 2002 decision to shift its vacuum cleaner manufacturing to Malaysia with a loss of hundreds of jobs.
Mr Dyson said; "We manufacture where our suppliers are in South East Asia and Singapore."
He added that his family and firm paid UK taxes.  In the past there have been reports of schemes being set up in locations including Malta for tax purposes, then wound down.
"It's quite clear and quite simple," Mr Dyson said. "Our companies are based here in Britain, I and my family are based here in Britain, and we all pay British taxes. We paid £330m in the last three years.
"We have no companies based offshore at all now," he added
Arlene Foster has had her first meetings since becoming first minister with the Northern Ireland secretary and the Irish foreign minister.
[NEXT_CONCEPT]
James Dyson has told the BBC it's important to keep engineers in the UK to produce hi-tech exports, as he announced a £1bn investment in research and development.