This was after chaotic scenes in which opposition legislators, citing a threat to civil liberties and free speech, threw books at the Speaker, shouted, chanted and sprinkled water over his deputy.
Television footage showed legislators exchanging blows in the public gallery before the vote.
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President Uhuru Kenyatta has faced mounting pressure to boost security since a 2013 attack by Somali al Shabaab rebels on a Nairobi mall that killed 67 people. The militant Islamist group killed more that 60 people in two attacks this month.
The new measures will allow suspects to be held without charge for 360 days, up from 90 days, compel landlords to provide information about their tenants and punish media organisations if they print material "likely to cause fear or alarm".
They measures take effect when Kenyatta signs them into law.
DIGNITY OF PARLIAMENT
Speaker Justin Muturi twice suspended the morning session after opposition legislators shouted him down.
During the afternoon session, television footage showed an opposition lawmaker sprinkling water from a bottle on deputy speaker Joyce Laboso, who was reading out the proposed changes to existing security law.
When Muturi took over the reading, opposition legislators jeered and hurled hard cover books, forcing him to duck.
"The dignity, the integrity of parliament is at stake. The cameras of the National Assembly will bear testimony to what I am saying," Aden Duale, the majority leader from Kenyatta's Jubilee coalition, said trying to calm the legislators.
"This is autocratic leadership," opposition MP John Mbadi told Reuters via telephone.
Some legislators had torn up parliamentary order papers that set the official agenda and scattered the pieces across the floor as they hugged each other and sang: "Msilale bado mapambano", Swahili for "Do not sleep, the struggle goes on".
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Muturi ordered parliamentary guards to escort some opposition members out of the assembly, shouting "Order!, order!, even as mapambano goes on, there will be order".
Armed police arrested activists protesting against the new law outside parliament.
Nine foreign missions in Kenya, including those of the United States, Britain, France, Germany, Canada and Australia, said in a statement on Wednesday they supported plans to improve security but said human rights should also be respected.
Legislators from both sides of the House approved the appointment by Kenyatta of opposition MP Joseph Nkaissery as the new interior minister. A retired major-general, Nkaissery faces the task of tackling al Shabaab's incursions from Somalia.