By Sara Sjolin, MarketWatch

LONDON (MarketWatch) -- European stock markets moved firmly higher on Tuesday as investors welcomed signs U.S. lawmakers are making progress in hammering out a fiscal deal and Germany's DAX 30 index flirted with an all-time high after upbeat data.

The Stoxx Europe 600 index rallied 0.8% to 314.71, on track for the highest closing level in almost a month.

Among notable movers in the index, shares of Rio Tinto PLC (RIO) gained 3.8% after the heavyweight miner said its iron-ore output rose to a new quarterly record.

Shares of Burberry Group PLC (BURBY) lost 5.2% after Apple Inc. (AAPL) named the luxury-goods firm's Chief Executive Angela Ahrendts as senior vice president of retail and online stores.

More broadly, investors in Europe welcomed developments in the fiscal negotiations in U.S., with the debt-ceiling looming and the government shutdown moving into Day 15. On the Senate floor on Monday, Senate Majority Leader Harry Reid said he was "very optimistic" about concluding deals "this week" to raise the debt limit as well as end the government shutdown. Sen. Mitch McConnell, the minority leader, said he shared Reid's feeling that "we'll get a result that's acceptable to both sides."

U.S. stocks rose on Monday, and futures also pointed to a higher open on Tuesday. Asia markets closed mostly higher.

German data further provided investors with a reason to celebrate. The ZEW sentiment survey showed that the economic expectations indicator rose further above its long-term average in October, to 52.8 points from 49.6 points in September--beating economists' expectations for an unchanged reading.

Germany's DAX 30 index jumped 0.7% to 8,786.00, on track for the highest close on record.

The U.K.'s FTSE 100 index picked up 0.9% to 6,562.99, while France's CAC 40 index rose 0.5% to 4,245.75.

Shares of Ashtead Group PLC climbed 3.1% after J.P. Morgan Cazenove lifted the equipment-rental company to overweight from neutral.

Shares of Zurich Insurance Group AG added 1.4% after J.P. Morgan Cazenove upgraded the firm to neutral from underweight.

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