By Sara Sjolin, MarketWatch

LONDON (MarketWatch) -- European stock markets rose Tuesday, as investors largely shrugged off a partial shutdown of the U.S. government and instead mirrored gains in Asia.

The Stoxx Europe 600 index added 0.3% to 311.38, partly recovering from a 0.6% loss on Monday.

Shares of Telecom Italia SpA jumped 4.3% after Goldman Sachs reinstated coverage of the firm with a buy rating.

"We believe the proposed changes to TI's controlling shareholder structure may provide it an opportunity to delever its balance sheet, which could lead to a significant positive change in strategy," the analysts said.

Shares of Renault SA added 1.2% after data showed new French car registrations for the auto maker jumped 18% in September.

More broadly, investors took inspiration from Asia, where Japanese stocks ended in positive territory after Prime Minister Shinzo Abe announced plans to increased the nation's sales tax in efforts to help the country's public finances.

U.S. stock futures also pointed to a higher open, even as the lawmakers failed to agree on a budget for the new fiscal year before the deadline, prompting a partial closure of the government. The shutdown is the first since 1996 and will leave thousands of government workers furloughed and national parks closed. Other services, including the issuing of Social Security checks and the U.S. Mail, will continue.

"It is not a wise idea for the politicians to play with the fragile recovery and especially the pace that they are playing with, as this could easily derail the recovery," said Naeem Aslam, chief market analyst at Ava Trade, in a note.

"The hope is that both the Democrats and the Republicans would come to their senses soon enough to see what the consequences could be on the markets by passing the temporary budget which could let the government run in the [meantime]," he added.

Back in Europe, data confirmed that the euro zone's manufacturing sector expanded for a third straight month in September, with the purchasing managers' index coming in in line with a preliminary estimate of 51.1, but lower than the 51.4 August print. A reading above 50 signals expansion.

Meanwhile, Eurostat said unemployment in the currency union edged lower for a third straight month in August, although not enough to affect overall the unemployment rate, which held steady at 12%. The July joblessness rate was revised lower after previously being reported at 12.1%, which means the 12% rate was the lowest since December 2012. Germany's unemployment unexpectedly rose to 6.9% in September.

"We see little momentum in the labor market picture at the aggregate level. This reflects our view that although a recovery in the euro area is well under way, it will take time for the rebound in sentiment to feed through to actual hiring decisions," said Timo del Carpio, European economist at RBC Capital Markets, in a note.

Most country-specific indexes, however, ignored the downbeat assessment and moved higher. France's CAC 40 index rose 0.7% to 4,171.81, while Germany's DAX 30 index gained 0.5% to 8,639.53.

The U.K.'s FTSE 100 index fell 0.3% to 6,445.12. Shares of Unilever PLC (UL) weighed on the index in London, off 3.7%, after the consumer-products giant downgraded its sales-growth expectations for the third quarter due to a slowdown in emerging markets.

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