"Ireland's always been appealing as an entry point (to Europe) for American companies," said Ric Hubler, director of global business growth, of the Metro Atlanta Chamber.
Gleeson called the current corporate tax rate "rock solid" despite worries it might be raised. Irish officials have said they would maintain the current tax rate.
"At the end of the day, what we're saying is that the underlying factors that have made for a very strong economic relationship between Ireland and the U.S. continue to apply," Gleeson said.
Some issues of importance to businesses have gotten better in Ireland, he added.
"Wage competitiveness has improved hugely," he said. "We had government (worker) pay cuts of an average of 14 percent already. That has had a big impact on pay cuts in the private sector as well. Companies looking to invest in Ireland are getting much better bang for their buck now."
Besides facilitating business relationships between Ireland the U.S., Gleeson's mission, which has a four-year term, includes promoting tourism and educational opportunities in Ireland.
While the economic crisis has brought Ireland unwanted attention, Gleeson looks forward to a more stable time.
"To some degree we may need for the current saturation (media) coverage to abate." Then, he said, "we can restore a little bit of that perspective and a little bit of that calm."