The 19A amendment was introduced after last week's aborted attempt caused due to disruption by supporters of former president Mahinda Rajapaksa.
"It has always been my desire to prune presidential powers. You all will agree that I have been very generous," Sirisena told the House.
Sirisena's opposition coalition had pledged to do away with presidential authority to make parliament more powerful, as their main plank in the January 8 presidential election which resulted in a stunning defeat for Rajapaksa.
Sri Lanka switched to an executive president-headed government in 1978 from a Westminster-style system.
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The 19A ran into a snag as some of its key provisions transferring powers of the president to parliament were subject to a national referendum by the Supreme Court.
As a result the government has been forced to leave out such provisions.
The version presented today will pave the way for the establishment of independent commissions to ensure good governance.
The vote on the amendment is to take place tomorrow.