In a last-minute broadcast urging MPs to legalise assisted dying, she rejected claims from ministers that the Bill is not sufficiently watertight.
Ms Leadbeater told Sky News: "I don't have any doubts whatsoever. I wouldn't put the Bill forward if I did.
"What I'm very clear about is we have got people now who the law is failing. We have got people taking their own lives.
"We have got families losing loved ones in very harrowing circumstances and we have got people having very painful deaths... so there is a very clear problem that needs to be solved.
"By creating a legal framework, we will improve the situation." MPs are due to vote on the Bill on Friday, with the party whips taking a back seat and allowing members to vote as they wish.
It is not known how the vote will go, with only a portion of MPs having publicly declared a preference.
The Cabinet itself remains divided, in spite of the Cabinet Secretary asking members not to get actively involved in the debate.
Fourteen members of the Cabinet, including the Prime Minister, are thought to be supportive of the Bill, while nine are opposed.
Yesterday, Work and Pensions Secretary Liz Kendall reiterated her support for assisted dying.
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