If all goes well during the "soft-play period" - open only to invited players - Internet gambling inside New Jersey will officially be open for business at 9 a.m. Tuesday.
In Lesniak's new proposal, companies operating under an international gaming license would not be able to accept U.S. customers.
Lesniak's bill would also allow sports betting from overseas.
Asked whether he had been in touch with overseas Internet-gambling firms about whether they were interested in coming to New Jersey, Lesniak said: "They reached out to me."
He would not say which companies had contacted him.
PokerStars, a top online site internationally, has attempted to participate in this week's launch of Internet gaming in New Jersey, but has so far been unsuccessful, according to industry news reports.
Lesniak's proposed bill would require the entire foreign betting operation to be located in New Jersey, but it would not have to be in Atlantic City.
Under New Jersey's existing Internet-gaming law, only Atlantic City casinos are allowed to obtain permits. All computer servers that will run the gambling sites must be located in the city.
Speaking after Lesniak at the news conference was Adam Ozimek, a senior economist at Econsult Solutions, who presented preliminary results of a study of the Internet-gambling market.
Ozimek said the global market was worth $10 billion annually and had been growing 17 percent annually, adjusted for inflation. Ozimek estimated that New Jersey could capture $2.2 billion to $3.8 billion of that international market and attract 4,700 to 7,900 jobs if Lesniak's bill became law.
A draft of the bill says the international Internet-gambling companies would pay a 10 percent tax on their gross revenue. Casinos in Atlantic City will pay a 15 percent tax on their gross revenue from intrastate Internet gambling.