White House spokesman Jay Carney said President Barack Obama had been briefed and that "we look to the Libyan government to fully investigate this killing".
In Tripoli, the foreign ministry denounced the "criminal act" and stated its "commitment to ensuring the security... of foreigners living in Libya".
State news agency LANA added that the ministry had confirmed it would "take all necessary steps to arrest those responsible and bring them to justice".
International School Benghazi director Adel al-Mansuri said Smith, who was married and the father of a two-year-old boy, had joined the faculty as a chemistry teacher late last year.
Mansuri said he had been set to return home next week for the year-end holidays.
He said Smith's wife and son were not in Libya.
The director added, without providing details, that another American teacher at the school had been taken to a secure location until he can travel home.
State Department deputy spokeswoman Marie Harf expressed "condolences to the victim's loved ones" and said "we are in contact with the family and are providing all appropriate consular assistance".
US Ambassador Deborah Jones added her condolences, saying on Twitter: "My heart goes out to the family of the American school teacher murdered today in #Benghazi.
"#Libya's enemies will not succeed in driving away her friends," she added.
Smith's death triggered an outpouring of emotion in Libya.
"It is with a very heavy heart that we announce the death of Ronnie Smith... shot & killed in #Benghazi," tweeted the Libyan Youth Movement.
"Ronnie was living and teaching in #Benghazi on his own accord, he told friends 'If I were to be killed, I will die for Education.'"
A Benghazi-based Twitter user identified as Taqwa Embasher posted: "Smith was a kindhearted, generous person. I was a target of his kindness and generosity. RIP my best teacher&friend."
International School Benghazi is one of the few foreign schools still operating in Libya, with most having shut down last year and this because of growing security problems.
Last year, the State Department warned US citizens against all but essential travel to Libya.
And in June this year, it advised against all travel to Benghazi, cradle of the 2011 NATO-backed revolution that ousted long-time dictator Moamer Kadhafi.
Violence largely blamed on jihadists
In other violence in Benghazi Thursday, three Libyan soldiers were shot dead in separate incidents, the latest of dozens of security personnel to be gunned down in recent weeks, security officials said.
A fourth soldier attached to military intelligence died when a bomb under his vehicle exploded, a security official said.
The violence rocking Benghazi is largely blamed on jihadist groups that have mushroomed since Kadhafi was toppled and killed.
Chief among them is Ansar al-Sharia, a group accused of the September 11, 2012 attack on the US consulate that killed Ambassador Chris Stevens and three other Americans.
Farther east, in the Islamist bastion of Derna, residents demonstrated Thursday against what they say is anarchy there and to demand a police and army presence.
On Monday, unknown gunmen fired on protesters in Derna, killing one and wounding seven, according to an updated toll given by a medic on Thursday.
Like Benghazi, Derna has seen a wave of killings of members of the security forces and the judiciary in attacks blamed on Ansar al-Sharia.
Prime Minister Ali Zeidan announced on Wednesday that preparations were under way to send troops to Derna, where law and order is almost non-existent.
Libya's new authorities have tried in vain to integrate former rebels who helped topple Kadhafi into the regular armed forces, with many militias carving out their own fiefdoms, each with its own ideology and regional allegiances.