Asian markets rallied on Monday, tracking fresh records on Wall Street, while the dollar held gains as Donald Trump's much-hyped tax cuts moved a step closer to being passed.

The controversial reforms look destined to become the US president's first major congressional victory as two key Republican holdouts in the Senate decided to back the bill after their demands were met Friday.

The news sent US stocks soaring on hopes the cuts will help fire the already healthy economy and boost company profits.

"The odds of the tax cut legislation getting passed within this year have grown," Shoji Hirakawa, chief global strategist at Tokai Tokyo Research Institute, told Bloomberg News.

This "will benefit not only the US, but also economies around the globe ... allowing investors to anticipate an increase in corporate earnings."