This was after Republicans from House of Representatives offered President Barack Obama a short-term increase in the debt limit to stave off default.
Stock indexes in Japan, Australia, China and Hong Kong all gained.
There have been concerns that a failure to agree a deal to raise the limit may see the US default on its payments and hurt the global economy.
Analysts said the offer by the Republicans had raised hopes that such a scenario was likely to be avoided.
“What this is, is opening the door to discussion and negotiation when before we had two sides just finger pointing,” said Peter Jankovskis, co-chief investment officer at OakBrook Investments LLC.
“We don’t know if in six weeks we’ll be in the same place, but at least this opens the possibility [of a deal]”, he said.
Japan’s Nikkei 225 index rose 1.5%, Hong Kong’s Hang Seng gained 1.3%, Australia’s ASX 200 added 1.6% and South Korea’s Kospi was up 1.2%.
On Thursday, the US markets had their best day since January 2013, buoyed by the proposal. The Dow Jones, S&P 500, and Nasdaq indexes all closed up by more than 2%.
The US needs to agree on raising the nation’s $16.69 trillion debt ceiling by October 17.
A failure to do so could see the US government default, as it runs out of money to pay its bills and service its national debt.
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