Opponents warned that the legislation, which has yet to receive final approval, will limit civic space in a country where the government is accused of crushing dissent and press freedoms.
The bill received 45 votes in a parliament that is heavily controlled by President Paul Kagame's ruling Rwandan Patriotic Front, and not a single vote was cast against.
It will now go to a parliamentary committee for further scrutiny.
The legislation seeks to impose strict rules on how NGOs are run and calls for them to submit their operating plans and budgets to the Rwandan authorities for approval.
"The bill will limit civic space because it gives the regulator the powers to interfere in day-to-day management of NGOs including firing staff," head of the Rwanda Civil Society Platform Joseph Nkurunziza told AFP.
He said he believed the bill was being rushed through as the presidential and legislative elections on July 15 mean parliament will be dissolved by mid-June.
One critic who declined to be named voiced concerns that the legislation could be used to intimidate civil society groups and deter them from scrutinising the polls and election bodies.
Kagame, Rwanda's de facto leader since the end of the 1994 genocide, is widely expected to win a fourth term in July.
In parliament on Thursday, Local Government Minister Jean Claude Musabyimana defended the bill, saying it will clamp down on "unserious" and "deceitful" organizations that do not deliver on their mandate.
"Their work has to be assessed; their budget has to be clear and show the activities they intend to do, so that we don't get unscrupulous organizations lying to people in order to benefit themselves," Musabyimana said.
Representatives of NGOs said they hope their input will be considered by the parliamentary committee, which is expected to study the bill in the next few days before it goes back to parliament for a final vote.
"In its current form, the draft law is problematic and indeed limits civic space in Rwanda," Andrews Kananga, executive director of the Legal Aid Forum, told AFP.
"But there is still a chance to change it through the parliament committee. I hope they listen."
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