"We have found no links with the group at this stage. Israel has mentioned this group but there is no conclusion yet that the men are members of the group," Paradorn Pattanatabut, secretary-general of the National Security Council, was quoted as saying by the Nation paper.
The suspects are still being questioned. Lebanon-based Hezbollah militant group has fought with Israel for years.
Sources identified the two men as Lebanese-French Daud Farhat and Lebanese-Philippine Yousef Ayyad.They were visited separately by Immigration Police and taken from their homes during the recent spring festival Songkran break.
"Their presence in Thai territory near the Jewish Passover, which this year fell on April 13, aroused the Thai side's suspicions, so the Thai side decided to take them into custody for questioning after a fatal shooting in the US during Passover," the source said.
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The pair are being detained under immigration laws as their visas were already revoked, the source said, while declining to add whether they would be deported.
Referring to news reports that there was a third Lebanese, the source said Bailal Bahsoun, who is also on the watch list, did not enter the country.