"We hope that Mr. Zakka's release is a positive sign for American detainees in Iran", it added, referring to several USA citizens who remain in detention in Iran.
Officials of the Foreign Ministry in Beirut were quoted as saying on June 4 that Iran had agreed to grant amnesty to Lebanese citizen Zakka, an information technology expert, it detained in 2015 for "collaborating against the state", according to Reuters.
Zakka was arrested in 2015 and convicted of spying for the US government - charges he denies.
Relatives of Zakka were also present at the presidential palace.
Both the Congress and the Senate passed resolutions in 2017 calling for the unconditional release of USA citizens and residents detained in Iran, including the Lebanese national.
Esmaili stressed Zakka's release was within "the frame of the law".
The Associated Press, citing a Lebanese official who spoke on condition of anonymity, reported that Zakka had been freed and was on a plane to Lebanon with Ibrahim.
He was arrested on the way to the airport and later sentenced to 10 years behind bars on espionage charges in a closed-door trial.
State TV later quoted an anonymous source as saying Zakka would be released on Tuesday afternoon and will be allowed to leave Tehran.
"Iran does not respect global agreements the least bit", he added.
"We're thankful for the release of the individual in Iran", press secretary Sarah Sanders said.
Iran's Revolutionary Guard detained Zakka in 2015 after he attended a conference in Tehran on the invitation of one of the country's vice presidents. The leader of the Iranian-backed Hezbollah has not made public comments about Zakka's imprisonment, but pro-Hezbollah media have said that Nasrallah had in recent days urged the Iranians to facilitate his release.
Zakka, who lives in Washington and holds resident status in the USA, leads the Arab ICT Organization, or IJMA3, an industry consortium from 13 countries that advocates for information technology in the region.
"This is in no way approved by the government", Molaverdi said.
Zakka has been imprisoned in Iran since 2015.
On May 11, Mr Aoun handed over a written letter to Mr Firouznia to be delivered to Iranian President Hassan Rouhani, repeating Lebanon's request for Mr Zakka to be freed at the end of Ramadan, the source said.