Kuwaiti lawmakers voted in favour of a legal amendment earlier this month, which could make insulting God and the Prophet Mohammad (PBUH) punishable by death
- Twitter is extremely popular in the Gulf state of 3 million and many public figures use the messaging site to debate politics, share gossip and advertise events.
Kuwait has so far used its criminal code to bring charges against individuals for slander or libel.
A court sentenced a Sunni Muslim writer to seven years in jail earlier this month and ordered that he pay nearly $18,000 in compensation after ruling that he had insulted Kuwait's Shi'ite Muslim minority on Twitter.
Police arrested a Kuwaiti Shi'ite last month, charging him with insulting the Prophet Mohammad on Twitter. He denied this, saying his account had been hacked, according to his lawyer.
Both cases triggered small street protests.
Kuwaiti MPs from across the political spectrum have voiced concern about sectarian tensions.
Shaikh Mohammad said laws regulating social media needed to be passed as soon as possible.
"I have been asking the parliamentarians to give this priority," he said on the sidelines of a parliament session, adding he hoped the measures would be implemented this year.
Islamist Member of Parliament Mohammad Al Dallal, who specialises in legal matters related to the media, said he thought the legislation could be passed as early as June given strong support among fellow deputies.
"Twitter is an open area ... everyone can speak. But it is not always being used as social media in Kuwait - not about friendship or personal matters but it is being used politically, to attack. This is a bad thing," he said.