Seamus McAleavey, chief executive of NICVA, the umbrella body for voluntary and community organisations in Northern Ireland, said poverty should be at the top of the agenda.
"We would like to see a strategy from the Executive to tackle poverty in inner city and rural areas," he said.
"There are a huge number of issues we think ultimately that cut across all departments and they all have a part to play. A strategy covers so may areas, such as energy, education and health.
"Fuel poverty has always been a significant issue and it's going to rocket up the agenda. People on low incomes end up spending a huge portion of their salary on fuel. Fuel poverty means people will die."
Nigel Smyth, director of CBI Northern Ireland, said promises must be kept. "We would like the Executive to deliver the goals set out in the Programme for Government," he said.
"The big focus is the economy, which has always been a central plank, including strategic issues such as productivity, the transport network, people, education and skills.
"Our members are concerned that all these big issues and the targets set around these are delivered.
"We believe Peter Robinson is very business-like, energetic and keen to deliver."
Peter Bunting, Assistant General Secretary of the Irish Congress of Trade Unions, said his concerns are primarily economic in nature.
"Mr Robinson needs to address the fault lines in the Northern Ireland economy," said Mr Bunting.
"He needs to ensure that the public services are protected not downsized, and that the marginalised in our society are catered for within that economic model.
"He should also disregard David Varney's latest review, which is more 'old hat'. "
Howard Wells, chief executive of the Irish Fooball Association, called for the new First Minister to tackle prominent sporting issues.
"I would like Mr Robinson to show some demonstrable leadership and to put sport high on the social agenda, as it's not anywhere on it at the moment.
"He also needs to make some positive decisions that benefit sport in terms of commitment to a new stadium and commitment to make public money available for football and sport in general."