A series of positive data out of Washington in recent weeks, particularly falling inflation, has been compounded by China's recent promises of stimulus measures to kickstart growth, as the country's post-Covid recovery grinds to a halt.
Traders are now keeping a close eye on earnings this week from tech titans Apple and Amazon, and US jobs at the end of the week that could provide an idea about the Fed's thinking.
Britain's central bank is also due to announce a rate decision.
On Monday, Chicago Fed boss Austan Goolsbee left open the possibility of pausing or stopping interest rate hikes at the bank's next policy meeting in September.
"Thus far we're on the golden path and we've got to walk that line," Goolsbee told Yahoo! Finance, referring to the path of lowering inflation without triggering a major recession.
He said the slowdown in inflation was "fabulous news", echoing comments from Minneapolis chief Neel Kashkari, who called the readings "quite positive".
"As we approach the middle of summer, there is a prevailing belief among people on the street that the Federal Reserve has probably made its final rate hike in the current cycle," said Stephen Innes of SPI Asset Management.
"This is due to the evident decrease in inflation pressures.
"The current economic conditions, including decreasing inflation, a pause in Federal Reserve tightening, and steady or increasing growth, could create an ideal situation for the stock market."
All three main indexes on Wall Street ended on a positive note, with the S&P 500 at a 16-month high.
But while Asia started the day on the front foot, some markets lost momentum.
Tokyo, Sydney, Seoul, Taipei and Manila rose but Hong Kong and Shanghai were dragged by profit-taking following a run-up last week.
Singapore, Wellington, Mumbai and Jakarta also fell, while London and Frankfurt opened lower. Paris was flat.
Data out of China showing the country's factory activity shrank last month reinforced expectations the government will continue to unveil economic support measures.
On Monday, officials announced a 20-point plan to boost consumption, touching on housing, culture and tourism.
The announcement comes after top leaders said last week the economy was facing "new difficulties and challenges" and agreed to "implement precise and effective macroeconomic regulation, strengthen countercyclical regulation and policy reserves".
With the mood among investors broadly positive, analysts who had warned of another tough week for markets were changing their outlooks.
Michael Wilson at Morgan Stanley had been downbeat but now sees more legs in the latest rally.
"The challenges companies have endured -- stubborn inflation, weak markets, and sluggishness internationally -- are no longer headwinds," he said.
"Now, we're not only seeing tailwinds heading into 2024, but we're getting less disruptive reactions in the stock market following earnings reports."
On currency markets, the yen weakened further as the Bank of Japan's decision to loosen its grip on monetary policy failed to provide support.
The central bank's tweak means its policy is still much looser than others and observers say it will likely be so for some time.
And the Australian dollar lost ground against its US counterpart after the country's central bank stood pat on interest rates again, with governor Philip Lowe saying previous hikes were "working".
- Key figures around 0715 GMT -
Tokyo - Nikkei 225: UP 0.9 percent at 33,476.58 (close)
Hong Kong - Hang Seng Index: DOWN 0.5 percent at 19,982.21
Shanghai - Composite: FLAT at 3,290.95
London - FTSE 100: DOWN 0.1 percent at 7,690.97
Dollar/yen: UP at 142.70 yen from 142.28 yen on Monday
Euro/dollar: DOWN at $1.0976 from $1.0997
Pound/dollar: DOWN at $1.2821 from $1.2834
Euro/pound: DOWN at 85.58 from 85.67 pence
West Texas Intermediate: DOWN 0.2 percent at $81.61 per barrel
Brent North Sea crude: DOWN 0.2 percent at $85.24 per barrel
New York - Dow: UP 0.3 percent at 35,559.53 (close)
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