In a letter of congratulations to the US president, Mr Higgins assured Mr Obama he has the continued goodwill and best wishes of the people of Ireland.
"The international community faces many daunting challenges and we look forward to your continued leadership and constructive engagement in the period ahead," wrote Mr Higgins, a human rights campaigner.
"The very close and warm relationship between Ireland and the United States has, with your help and encouragement, prospered during your tenure.
"I am confident that, under your leadership, our bilateral relations will be further advanced during the next four years.
"My wife Sabina and I send our warmest personal wishes to you and your family as you begin your second term."
Mr Gilmore said the strong trade relationship between Ireland and the USA was crucially important for our economic recovery.
"We are dependent on the American economy growing, so we have an interest in measures being taken that will expand the American economy and create jobs and improve trade," he said.
Mr Gilmore downplayed concerns that President Obama might take actions which would affect US multi-nationals based here.
"Although that was mentioned in his first term, it didn't materialise at all. I think that is because there is a recognition in the US administration that investment is a two-way street'" he told RTE's Morning Ireland.
Mr Gilmore said there were 100,000 jobs in US companies here but also 85,000 jobs created by Irish investment in the USA.
Elsewhere, Moneygall native Henry Healy said he was delighted for his eighth cousin, whom he also visited at the White House for St Patrick's Day.
He said Mr Obama had got a resounding 'Yes' from the American people to continue the progress that he has been making.