* KOSPI on track to post weekly gain

* Foreigners set for a 31st consecutive buying day

* Banks, securities rally on bullish Q3 earnings outlook

SEOUL, Oct 11 (Reuters) - Seoul shares climbed to their highest in seven months early on Friday, as politicians in Washington showed they were making progress in resolving a stalemate over the U.S. debt limit, helping to bolster investor risk appetite.

Gains were underpinned by offshore buying that stood at 104.6 billion won ($97.42 million) in the morning. Foreigners are on track to a 31st consecutive session of net butying. Institutions were also poised to snap a 21 consecutive session of selling by purchasing 78.9 billion won worth of local shares.

The Korea Composite Stock Price Index (KOSPI) rose 1.2 percent to 2,025.94. points by 0216 GMT after reaching as high as 2,027.23, its highest intraday level since March 6.

"Risk aversion is on the down for the moment as investors finally found light as progress was made, although the political cues from Washington show the issues have not been fully solved," said Bookook Securities analyst Kim Sung-hwan.

Kim added that the market's focus will gradually shift towards global economic recovery and corporate earnings.

House Republican leaders on Thursday offered a plan to extend the government's borrowing authority for several weeks, and the White House said it would consider the proposal, sparking a big rally on Wall Street.

But concerns were not fully relieved as The New York Times later reported President Barack Obama had rejected the plan, but Republican Paul Ryan told reporters Obama had neither accepted nor rejected the proposal.

In an interview with Reuters regarding the U.S. debt stalemate, South Korea's Minister of Strategy and Finance Hyun Oh-seok said he did not expect a "big effect" on the Korean economy if it was a short-term phenomenon.

The South Korean market responded positively to the overnight progress in Washington.

Among all sectors, banks and securities advanced the most, with Woori Finance Holdings Co Ltd and Hyundai Securities Co Ltd rising 5.8 percent and 5.2 percent, respectively, to outperform sector peers and the broader market.

The energy chemical sector and shipbuilding sector gained on prospects of better earnings, with Lotte Chemical Corp and Hyundai Mipo Dockyard Co Ltd gaining 4.8 percent and 3.2 percent, respectively.

Earlier in the day Hyundai Heavy Industries Co Ltd said it had won an $850 million order to build four liquefied natural gas (LNG) carriers from Malaysia's Petroliam Nasional Bhd (Petronas). The shipbuilder is up 1.1 percent.