Deputy Premier James Merlino failed in a bid to derail the controversial legislation when his amendment was voted down at 11.30pm on Wednesday.
The proposed laws to legalise euthanasia are now being debated and examined line-by-line.
"I'm very pleased and proud that we've passed the second reading, that hurdle if you like," Premier Daniel Andrews told reporters on Thursday.
But he will not support any of the 150 amendments.
"This is a good bill, it is the product of a long and considered process involving experts," Mr Andrews said.
"I don't reflect negatively on anyone who moves amendments, that is their right.
"(But) many of them will be moved by people, who even if those amendments were successful, would not vote for the bill."
Health Minister Jill Hennessy said the debate had been emotional, but had shown parliamentarians to be authentic and vulnerable.
"It's really hard to talk about death at the best of times but to debate significant reform about giving people a better death is really challenging but it can bring out the best in our parliamentarians," she told reporters.
"We're going to keep fighting hard to try and bring this home."
Mr Merlino, a fierce opponent of euthanasia, had put forward a amendment that would have derailed further debate on the bill and put it off indefinitely.
He told reporters on Thursday he was disappointed his motion failed, "but that's the nature of democracy and the debate".
"This euthanasia legislation is a recipe for elder abuse, the fact that we don't know what drugs are going to be used," Mr Merlino said.
The government hopes to vote on the legislation by the end of the week.
