In October, Mr Ponta indicated that Romania was also preparing to join Mr Blair's Global Network of Delivery Leaders, which aims to help members improve the "delivery" of services such as education, health and construction.
Tuesday's encounter, however, could prove awkward. On the same day the Romanian parliament approved controversial new changes to the country's criminal law to help protect MPs against corruption charges.
"It is very discouraging that these revisions were passed with no consultation, no debate, and no opportunity for judicial authorities or civil society to respond to the proposed amendments," said a statement released by the embassy.
"This move by the Parliament is a step away from transparency and rule-of-law and is a discouraging sign for investors, which will negatively affect Romania's economy."
It is not clear whether the discussion between Mr Obama and Mr Ponta, with Mr Blair looking on, strayed into such difficult territory.
All three men appear to be enjoying the encounter in a series of photographs published by Mr Ponta on his Facebook page.
It took place as a result of the Romanian prime minister approaching Mr Blair following the US president's emotive tribute to Mr Mandela, sources in Mr Ponta's entourage told Romanian media.
In the photographs Mr Blair can be seen apparently crouching down behind Mr Obama, who is seated, prompting the US president to turn around to greet him and to shake Mr Ponta's hand.
The US president is then pictured standing up talking to both men with Mr Blair's wife Cherie and Helle Thorning-Schmidt, the Danish prime minister, looking on.
Following a meeting with Mr Blair in October Mr Ponta indicated that Romania was preparing to join the Global Network of Delivery Leaders, a grouping formed by the former prime minister in New York amid a meeting of the UN's General Assembly.
The network, backed by the World Bank, currently comprises six countries including Albania, Malawi and Haiti.