The men were stopped by the police when they approached one of the guarded gates at the Vatican and asked to be let through to the Institute for Religious Works (IOR) as the bank is formally known, Vatican spokesman Federico Lombardi told AFP.
The bonds were discovered in a briefcase they were carrying and the men were handed over to Italy's financial police, who found false passports and other fake documents in their hotel rooms.
The haul came a day after Italian prosecutors said two former top executives at the Vatican bank will go on trial for money laundering in a case that led to the seizure of €23 million ($32 million).
IOR press officer Max Hohenberg said the American and Dutch man "are neither clients of the bank, nor were they expected".
The bank, which handles the accounts of Catholic clerics and congregations around the world, has a murky reputation but the Vatican has vowed to clean it up and bring it in line with international laws.
Lombardi said Saturday's episode "shows the controls are working. But I don't think we're talking about a plot by criminal masterminds if they managed to get caught at the first hurdle."
The IOR has a troubled history, including the collapse of the Banco Ambrosiano, in which the Holy See was the main shareholder, and which had been accused of laundering money for the Sicilian mafia.
The chairman of Banco Ambrosiano, Roberto Calvi — dubbed "God's Banker" in the press — was found hanging from Blackfriars Bridge in London in 1982 in a
suspected murder by mobsters.
In February, Pope Francis created a new finance ministry to oversee the Holy See's economic affairs in a move the Vatican said was aimed at increasing transparency.