Washington - President Donald Trump on Saturday hailed the tax cut bill passed by the Senate overnight, the latest step toward what could be a major victory for his legislative agenda.

In an early morning Twitter post, Trump called his bill the biggest tax cut in US history and said his Republican Party would now work with the House of Representatives, which has passed its own tax bill, to produce a common version.

"Thank you to House and Senate Republicans for your hard work and commitment!" Trump wrote.

After a marathon session that stretched into the night, the chamber voted 51 to 49 in favour of the country's largest tax overhaul in 31 years, overcoming stubborn internal Republican resistance and dismissing angry criticism from Democrats over last-minute revisions to the bill.

The Senate version and the one passed recently by the House must now be reconciled into a single bill and approved again by both chambers, before it can be signed into law.

Both versions lower the corporate tax rate from 35% to 20% and include more modest tax cuts aimed at individuals across all income levels.