The Republican-led US Senate has approved the most sweeping rewrite of the nation's tax laws in more than three decades, a deeply unpopular bill they say Americans will learn to love when they see their paychecks in the new year.

Key points: Bill will be sent back to the US House of Representatives for a final vote

Bill will be sent back to the US House of Representatives for a final vote Republicans say changes will provide "real tax relief" for most Americans

Republicans say changes will provide "real tax relief" for most Americans The package will cost US$1.5 trillion and push national debt higher

US President Donald Trump cheered the lawmakers on, eager to claim his first major legislative victory.

The Senate narrowly passed the legislation 51-48, with all Republicans in favour and all Democrats opposed, shortly after midnight.

Protesters chanted "kill the bill, don't kill us" as the legislation passed, with US Vice President Mike Pence repeatedly calling for order.

However, it was not the final word in US Congress because of one last hiccup: three provisions in the bill, including its title, violated Senate rules, forcing the Senate to vote to strip them out.

The massive bill was sent back to the House of Representatives for a final vote, and Republicans will get a chance to celebrate again.

Hours earlier, US House Speaker Paul Ryan, who has worked years toward the goal of revamping the tax code, gleefully pounded the gavel on the House vote.

GOP House members roared and applauded as they passed the US$1.5 trillion ($1.96 trillion) package that will touch every American taxpayer and every corner of the US economy.

Republicans say the changes will provide tax relief for most Americans and boost economic growth, but Democrats say it is a give-away to corporate America and the super-rich.

The bill would slash the corporate income tax rate from 35 per cent to 21 per cent. The top tax rate for individuals would be lowered from 39.6 per cent to 37 per cent.

The legislation repeals an important part of the 2010 health care law known as Obamacare — the requirement that all Americans carry health insurance or face a penalty — as the GOP looks to unravel the law it failed to repeal and replace this past summer.

It also allows oil drilling in the Arctic National Wildlife Refuge.

'Real tax relief', or 'messing up America'?

Despite Republican talk of spending discipline, the bill will push the huge national debt ever higher.

"This was a promise made. This is a promise kept," Mr Ryan and other GOP leaders said at a victory news conference.

After the delay for a second House vote, the measure then heads to Mr Trump, who is aching for a big political victory after 11 months of legislative failures and nonstarters.

The President tweeted his congratulations to GOP leaders and to "all great House Republicans who voted in favour of cutting your taxes!"

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Congressional Republicans, who faltered badly in trying to dismantle Barack Obama's Affordable Care Act, see passage of the tax bill as crucial to proving to Americans they can govern — and imperative for holding onto House and Senate majorities in next year's midterm elections.

"The proof will be in the paychecks," Senator Rob Portman said during the Senate's night-time debate.

"This is real tax relief, and it's needed."

But the top Senate Democrat disagreed.

"This is serious stuff. We believe you are messing up America," New York Senator Chuck Schumer told Republicans, chiding them for not listening to his remarks.

The GOP has repeatedly argued the bill will spur economic growth as corporations, flush with cash, increase wages and hire more workers.

But they acknowledge they have work to do in convincing everyday Americans.

Many voters in surveys see the legislation as a boost to the wealthy, such as Mr Trump and his family, and a minor gain at best for the middle class.

The bill would initially provide tax cuts for Americans of all incomes.

AP