He also apologized for the crisis during his annual State of the State speech Tuesday night.
The Republican governor has become a lightning rod for criticism because the crisis unfolded under the state's watch.
"To begin, I'd like to address the people of Flint. Your families face a crisis, a crisis you did not create and could not have prevented," Snyder said. "I am sorry and I will fix it."
The additional money would go to help fund the following, the governor said:
- Bottled water, filters, replacement filters;
- Assistance to Flint to help with utility-related issues;
- Testing and replacing fixtures in schools and other high-risk locations;
- Treatment of children with high lead levels;
- Services for the treatment of potential behavioral health issues;
- Support for children and adolescent health centers;
- An infrastructure integrity study for pipes and connections.
Snyder spoke about the long-term consequences of the crisis, saying the $28 million request won't be the last budget request for Flint.
He also released a detailed timeline of steps officials have taken already and announced he will be releasing his 2014 and 2015 emails related to the crisis.
"No citizen of this great state should endure this kind of catastrophe. Government failed you -- federal, state and local leaders -- by breaking the trust you placed in us," Snyder said.
"You deserve better. You deserve accountability. You deserve to know that the buck stops here with me. Most of all, you deserve to know the truth."
The governor's address did little to quiet his critics.
"For those who think $28 million will begin to remedy the Flint water crisis, that is a fraction of the money city residents have paid for poisoned water that they cannot drink," said Democratic U.S. Rep. Dan Kildee.
Flint Mayor Karen Weaver has previously said the costs to undo the damage, both to infrastructure and residents' health, could be between $1 billion and $1.5 billion.
"Flint deserves an immediate response equal to the gravity of this ongoing public health emergency. A state-appointed emergency financial manager created this problem and the state must step up and do more to help Flint families and children right now," Kildee said.
Outside where the governor spoke in Lansing, protesters gathered and demanded that Snyder step down.
Tomeko Hornaday has been a resident of Flint for some 40 years. She said what's happened there is an embarrassment.
"Just to see the city of Flint just go down for the last decade, you know, with the crime, with no jobs, all the way down to us not having any water," Hornaday said. "We're angry. We want something done."
In April 2014, the state, which had appointed an emergency manager to Flint amid a financial crisis, decided to temporarily switch Flint's water source to the Flint River as a cost-saving measure until a new supply line to Lake Huron was ready.
The Flint River had long had a reputation for nastiness when the state made the switch, and a 2011 study had found that before water from the Flint River could be considered potable, it would need to be treated with an anti-corrosion agent, a measure that would have cost the state about $100 a day.
Experts say that water treatment would have prevented 90% of the problems with Flint's water.
After the switch, residents complained their water looked, smelled and tasted funny.
Virginia Tech researchers found the water was highly corrosive. A class-action lawsuit filed last year alleges the state Department of Environmental Quality didn't treat the water for corrosion, in accordance with federal law, and because so many service lines in Flint are made of lead, the noxious element leached into the water of the city's homes.
The city swapped back to the Lake Huron water supply in October, but the damage was already done to the lead pipes. The state is now handing out filters and bottled water with the help of the National Guard.
An attorney representing Flint residents who are suing Michigan officials over what his legal team calls the city's "lousy, no-good water" has a message for state officials targeted in the lawsuits: "Don't fight it."
The state is responsible for the water woes Flint residents have suffered and continue to suffer as a result, and the only responsible thing the state can do is own up to it, attorney Michael Pitt said.
"If you make the mess, you clean it up," he said. "I'm reminding our elected officials of what my kindergarten teacher told me."
The three lawsuits seek individual damages for Flint residents -- an estimated 500 and counting -- who have complained of health issues and worry about future ailments as a result of the state swapping the city's water source from Lake Huron to the notoriously filthy Flint River in 2014.
Bill Goodman, another member of the legal team, explained to reporters the purpose of the three lawsuits: The federal lawsuit filed in November addresses alleged violations of the U.S. Constitution; the suit filed last week in the Michigan Court of Claims targets alleged violations of the state constitution; and the suit filed in Genesee County Circuit Court deals with what he called "grossly negligent actions by government officials."
'Stuff is revealed'
During the discovery process, Goodman said, attorneys and their clients should receive within six weeks emails and other documents from various government officials, including Snyder, that could shed light on a critical yet heretofore unanswered question: How the heck did this occur?
"We finally find out what happened. Stuff is revealed that hasn't been revealed," he said.
Pitt added that the response to the federal lawsuit is due February 1, and that may provide some answers, but he encouraged state leaders to act promptly in providing money to residents who have been inconvenienced, sickened or worse by the water debacle.
"They need financial aid. Water's great. Filters are great," he said. "But our people need financial aid, and they need it now."
He further lambasted state officials who, he alleged, learned of elevated lead levels in children's blood in 2014 and did nothing.
"They were staring at a public health emergency, and they sat on it for over 10 months," he said, further criticizing leaders who assured residents the water was safe when they knew it wasn't true.
"I don't know how many kids were poisoned because of these false assurances, but we're going to find out."