WASHINGTON (AP) -- Congress approved long-sought legislation Tuesday to make firing employees easier for the Department of Veterans Affairs, part of an effort urged by President Donald Trump to fix a struggling agency serving millions of veterans.

The House cleared the bill, 368-55, replacing an earlier version that Democrats had criticized as overly unfair to workers. The Senate passed the bipartisan legislation by voice vote last week. It will go to Trump later this week for his signature.

The measure comes after a 2014 scandal at the Phoenix VA medical center, where some veterans died while waiting months for appointments. During the presidential campaign, Trump promised to fire VA employees "who let our veterans down," describing the government's second-largest agency and its more than 350,000 employees as "the most corrupt" and "incompetent."

Rep. Phil Roe, R-Tenn., who chairs the House Veterans Affairs Committee, said the legislation was a necessary first step in overhauling the VA. Congress will soon take up legislation to give veterans expanded access to doctors outside the VA.

"For far too long, the failures of the bad actors have tarnished the good name of all VA employees," Roe said. "No effort toward real, wholesale reform at the department will ever be successful absent a strong culture of accountability first."

The House vote came as federal investigations into possible collaboration between the Trump campaign and Russia continued to hang over much of Washington, largely stalling the administration's biggest legislative initiatives. Attorney General Jeff Sessions testified Tuesday before a Senate panel on Russia contacts as House members took up the VA bill.

House leaders were quick to tout progress on veterans' issues.

"We've been talking about this for about three years. And we uncovered all the scandals at the VA. Now we're making law," said House Speaker Paul Ryan, R-Wis. "Now we're getting the veterans the kind of response and the kind of accountability they earned and deserved."

The bill was backed by VA Secretary David Shulkin, who called the employee accountability process "clearly broken." It would lower the burden of proof to fire employees, allowing a dismissal even if most evidence is in a worker's favor.

The American Federation of Government Employees, the largest federal employee union, opposed the bill. But the Senate-passed measure was viewed as more in balance with workers' rights than a version passed by the House in March, mostly along party lines. The Senate bill calls for a longer appeal process than the House's version -- 180 days vs. 45 days. VA executives would be held to a tougher standard than rank-and-file employees.

The Senate bill also would turn a campaign promise of Trump's into law. It would create a permanent VA accountability office, established in April by executive order.

The VA has been plagued for years by problems, including the 2014 scandal, where employees created secret lists to cover up delays in appointments. Critics say few employees are fired for malfeasance.

Trump praised the legislation when it passed the Senate last week, urging the House on Twitter to "get this bill to my desk ASAP!" House Majority Leader Kevin McCarthy, R-Calif., promised to get it done this week.

Veterans' groups cheered the bill.

"Veterans across the country can look forward to a new culture of accountability and integrity at the VA," said Dan Caldwell, policy director of the conservative Concerned Veterans for America, which lobbied for years to pass legislation.