The Senate gave final approval to a measure eliminating a rule to prevent coal mining debris from being dumped into nearby streams, while the House approved a separate resolution doing away with extended background checks for gun purchases by some Social Security recipients with mental disabilities.
The Senate's 54-45 vote sends the repeal of the stream protection rule to Trump, who is expected to sign it.
The Interior Department said in announcing the rule in December that it would protect 6,000 miles of streams and 52,000 acres of forests, preventing coal mining debris from being dumped into nearby waters.
The vote was the first in a series of actions Republicans are expected to take in coming weeks to reverse years of what they call excessive regulation during President Barack Obama's presidency. Rules on fracking, federal contracting and other issues also are in the cross-hairs as the GOP moves to void a host of regulations finalized during Obama's last months in office.
Senate Majority Leader Mitch McConnell, R-Ky., called the stream rule "an attack against coal miners and their families" and said it would have threatened coal jobs and caused major damage to communities in Kentucky and other coal-producing states.
"The legislation we passed today will help stop this disastrous rule and bring relief to coal miners and their families," McConnell said.
Democrats called the vote an attack on clean water and a clear win for big coal-mining companies and other polluters.
Sen. Maria Cantwell, D-Wash., said the stream rule had nothing to do with the decline of coal, which faces stiff competition from cheap natural gas.
"This rule was not in place" when coal production began declining in the past half-dozen years, Cantwell said. The rule "has nothing to do with what has happened in the marketplace as natural gas has become a more viable option than coal," she said.
In the House, the issue was an Obama rule extending background checks for disabled Social Security recipients mentally incapable of managing their own affairs. The vote was 235-180.
Under the rule, the Social Security Administration would provide information to the gun-buying background check system on recipients with a mental disorder so severe they cannot work and need someone to handle their benefits. The rule, finalized in December, affects an estimated 75,000 beneficiaries.
Republican lawmakers criticized the regulation for reinforcing a negative stereotype that people with a mental disorder are dangerous.
"There is no evidence suggesting that those receiving disability benefits from the Social Security Administration are a threat to public safety," added Rep. Bob Goodlatte, R-Va., chairman of the House Judiciary Committee.
"Once an unelected bureaucrat unfairly adds these folks to the federal background check system, they are no longer able to exercise their Second Amendment right," he said.
After the 2012 school massacre in Newtown, Connecticut, Obama directed the Justice Department to provide guidance to agencies regarding information they are obligated to report to the background check system.
In Newtown, 20 children and six educators were shot to death when a gunman entered the Sandy Hook Elementary School on Dec. 14, 2012. The gunman had earlier killed his mother inside their home, and he used a gun and ammunition that she had purchased. His mental health problems have been extensively reported since the shooting.
Democrats said Republicans were doing the bidding of the National Rifle Association, which opposed the Social Security Administration's rule. Rep. Jim McGovern, D-Mass., said his constituents have a right not to be victims of gun violence.
"They have a right to protect their loved ones who may use a weapon against themselves or their family members," McGovern said.
The Social Security Administration regulation also established a process for people to appeal having their names submitted to background check database. But attorneys general from a dozen states wrote to congressional leaders and said such appeals can take months or years to resolve. They said the regulation violates basic notions of due process by permitting an agency to revoke someone's Second Amendment rights without a hearing.
Republicans are employing a rarely used tool to roll back some of the rules issued in the final months of Obama's tenure. The Congressional Review Act provides a temporary window for a simple majority of both chambers to invalidate the rule. Trump would also have to sign the disapproval measure for a regulation to be deemed invalid.
The law also prevents the executive branch from imposing substantially similar regulations in the future.