By Sara Sjolin, MarketWatch

LONDON (MarketWatch) -- European stocks pushed higher on Friday, driven by optimism over U.S. debt talks, with the benchmark index for the region looking to its first weekly gain, albeit small, in three weeks.

The Stoxx Europe 600 index climbed 0.3% to 311.23, setting it on track for a 0.4% gain on the week.

On Thursday, the index rallied 1.7% on signs U.S. lawmakers were moving closer to agreeing on a deal to lift the country's debt ceiling. The U.S. government, meanwhile, has been shut down for 11 days.

House Republicans on Thursday proposed a six-week extension to the borrowing limit, in efforts to avoid a default on Oct. 17 -- the date Treasury Secretary Jack Lew said is the deadline for raising the debt limit. House Republican leaders and President Barack Obama ended a roughly 90-minute meeting at the White House late Thursday without a deal to either raise the debt limit or reopen government, but with a plan to keep talking.

U.S. stocks rallied on Thursday, with the Dow Jones Industrial Average (DJI) putting in its best one-day point gain since December 2011. But Wall Street stocks opened with just mild gains on Friday.

"[There's] nothing concrete, but the fact they are talking is a step in the right direction compared [with] the recent flat refusals to give any ground. [Are] Republicans finally softening, after being apportioned with more of the blame?" said Mike van Dulken, head of research at Accendo Markets, in a note to clients.

Among country-specific indexes in Europe, the U.K.'s FTSE 100 index rose 0.7% to 6,474.13, while Germany's DAX 30 index added 0.2% to 8,706.61, on track for an all-time closing high.

France's CAC 40 index was one of the few indexes heading the other direction, flat at 4,214.85.

Shares of Royal Mail PLC soared 33% to 4.39 pounds ($6.95) on its first trading day. The initial-public-offering price was GBP3.30 a share, and the solid interest on the first trading day fueled suggestions that the previously state-owned company was sold off too cheap.

Elsewhere, shares of Royal Philips NV gained 2.8% after Goldman Sachs lifted the electronics firm to buy from neutral. The analysts said they saw the Dutch firm as one of a few remaining stocks with re-rating potential within "capital goods." "We expect its steady progress towards higher margins and returns, better cash quality and more predictable earnings to be rewarded through multiple expansion," they said.

On a more downbeat note, shares of Geberit AG lost 2.6% after Goldman Sachs cut the toilets and sanitary piping-system maker to sell from neutral on concerns it will "struggle to outgrow the underlying market in its most profitable segment."

Shares of Neste Oil Oyj slid 5.6%. UBS lifted shares to neutral from sell, but also said it sees net income flat over 2014-17.

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