Following the meeting, Rep. and Vice Chair of the House Republican Conference Lynn Jenkins, said, "Opening the government is a negotiation that will happen tonight [Thursday night] and in the hours ahead, we hope to have it open by Monday night."
(Read more: No deal yet: White House)
Hopes of an end to the political stalemate saw Wall Street rally more than 2 percent overnight. The Dow catapulted 323 points while the CBOE Volatility Index (VIX), considered the best gauge of fear in the market, tumbled to 16.29 after hitting a seven-week high of 21 this week.
Nikkei 1.5% higher
Japanese traders took their cues from a weaker currency after dollar-yen climbed above the 98 handle, rebounding from a two-month low hit this week.
The index hit its highest level since October 2 thanks to strong gains in blue-chip exporters. A depreciating currency boosts their competitive advantage in overseas markets. Camera maker Nikon and robotics maker Fanuc rose over 4 percent each.
But index heavyweight Fast Retailing, owner of the Uniqlo clothing chain, shed over 3 percent after its full-year operating profit came in below its target.
(Watch now: Japan official: Economy needs corporate tax cuts)
Shanghai adds 1.7%
China's benchmark index hit a new two-and-a-half week high in afternoon trade after Premier Li Keqing hinted of a positive third-quarter GDP report, due October 18.
Sentiment also rose on news that Beijing has launched a currency swap deal with the euro zone in the country's latest push to transform the yuan into a major world currency.