The two are also suspected of violating a law prohibiting groups such as al-Qaeda and the so-called Islamic State (IS), the statement added.
Geneva's prosecutor said traces of explosive had been found in their car.
Geneva has been on high alert this week amid fears an IS cell was in the area.
Swiss President Simonetta Sommaruga said on Friday that a "foreign authority" had provided the information about "a potential IS cell in the Geneva area" but there was no indication that "a concrete attack" was planned.
Geneva's Prosecutor Olivier Jornot told a news conference on Saturday that the two Syrians had just arrived in the Swiss city and could not speak French.
He said although traces of explosives were found in their car during their arrest on Friday, there was no evidence of toxic gas.
An earlier statement from the prosecutor's office said criminal proceedings and been opened against them under Switzerland's law against the manufacture and transport of explosives and toxic gases.
The tip-off about a terror cell in Geneva had originally come from the United States, Swiss media reported on Friday.
Daily newspaper Le Temps, quoting a source close to the investigation, said US intelligence had identified three jihadist cells in Chicago, Toronto and Geneva.
On Thursday, security was stepped up outside synagogues, the UN building and the French ambassador's home, as well as train stations, the airport and similar places.
The number of police on Geneva's streets has been increased.
UN spokesman Michele Zaccheo said there was "no specific threat to the UN in Geneva or its personnel".
The border with France runs through the outskirts of Geneva.
IS said it carried out the attacks in Paris on 13 November which killed 130 people.
Two men linked to the attacks - Salah Abdeslam and Mohammed Abrini - are still on the run and investigations have been launched in several European countries.
Two people of Syrian origin have been arrested in Geneva on suspicion of making, concealing and transporting explosives, the Swiss attorney general says.