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* Energy firms rise as oil prices gain
* Apple supplier Skyworks gains on upbeat Q2 results
* U.S. service sector activity contracts in April-ISM
* Indexes up: Dow 1.34%, S&P 500 1.45%, Nasdaq 1.69% (Updates to open)
By Medha Singh and Shreyashi Sanyal
May 5 (Reuters) - U.S. stock indexes jumped on Tuesday as a recovery in oil prices lifted battered energy stocks and a slew of countries eased coronavirus-induced restrictions in an attempt to revive their economies.
Some hard-hit countries, including Italy, as well as a handful of U.S. states are tentatively easing stay-at-home orders this week, raising hopes for a recovery in oil demand.
All the major S&P 500 sub-indexes were trading higher, led by a 3.6% advance in the energy sector, but the index is still the top loser across sectors with a 35% decline this year.
Market-leading growth stocks such as Microsoft Corp , Amazon.com Inc and Apple Inc rose for a second day, helping offset concerns about the latest U.S.-China spat over the origin of the novel coronavirus.
The S&P 500 has climbed about 30% from its March lows on the back of unprecedented stimulus measures and signs of a plateau in new COVID-19 cases in many parts of the world.
"There's a growing sense that the worst for the global economy is right now, while lockdowns are in place and coronavirus treatments are unproven," said Jasper Lawler, head of research at London Capital Group.
"It follows that it only gets better from here as lockdowns ease and treatments are found."
However, many market experts have warned the rally could be tested amid a risk of another wave of virus infections and with growing evidence of the damage to the economy and corporate America.
Data on Tuesday showed the domestic services sector recorded its first contraction in nearly 10-1/2-years, while the Institute for Supply Management's (ISM) non-manufacturing index showed a smaller-than-expected decline.
All eyes will now be on the Labor Department's report of monthly nonfarm payrolls due Friday.
"It's all about the mood swings and hopes of the economies reopening. But the problem is this could change once we get to see some of the hard numbers, especially the employment report," said Peter Cardillo, chief market economist at Spartan Capital Securities in New York.
With more than half of the S&P 500 companies reporting so far, first-quarter earnings are expected to have fallen 12.5%, with analysts expecting an earnings recession by the second quarter, according to Refinitiv data.
At 10:12 a.m. ET the Dow Jones Industrial Average was up 317.97 points, or 1.34%, at 24,067.73, the S&P 500 was up 41.19 points, or 1.45%, at 2,883.93 and the Nasdaq Composite was up 147.46 points, or 1.69%, at 8,858.18.
Apple supplier Skyworks Solutions Inc gained 8.1% after reporting upbeat quarterly results, but warned of a hit from the pandemic in the current quarter.
Pfizer Inc rose about 2.3% after announcing that a venture with its German partner had started delivering doses of its experimental coronavirus vaccines for human testing in the United States.
Advancing issues outnumbered decliners more than 5-to-1 on the NYSE and 4-to-1 on Nasdaq.
The S&P index recorded five new 52-week highs and no new low, while the Nasdaq recorded 36 new highs and two new lows. (Reporting by Medha Singh and Shreyashi Sanyal in Bengaluru; Editing by Anil D'Silva, Saumyadeb Chakrabarty and Shounak Dasgupta)