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* Weekly jobless claims fall, Q1 GDP unrevised at 6.4%

* Tesla shares boost Nasdaq, S&P 500

* Lilly jumps on plan to seek approval for Alzheimer's drug

* Indexes: Dow +1.04%, S&P 500 +0.66%, Nasdaq +0.72%

June 24 (Reuters) - The Nasdaq and the S&P 500 indexes hit all-time highs on Thursday, with the Dow also jumping, as U.S. President Joe Biden embraced a bipartisan Senate infrastructure deal.

After the U.S. economy grew at a 6.4% annualized rate in the first quarter, thanks to the massive fiscal stimulus, investors have been banking on an infrastructure agreement that could steer the next leg of the recovery for the world's largest economy.

Caterpillar jumped 3.4% and Boeing rallied 2.2%, helping lift the Dow Jones Industrial Average.

"In the short term, I think there will be some 'buy the rumor and sell the news' in materials and industrials, but as we start to see more details come out about how the money will be spent, I think we will get a continued benefit," said Sal Bruno, chief investment officer at IndexIQ in New York.

Tesla Inc rose 5% after Chief Executive Officer Elon Musk said he would list SpaceX's space internet venture, Starlink, when its cash flow is reasonably predictable, adding that Tesla shareholders could get preference in investing.

Mega-caps Microsoft Corp, Netflix Inc and Facebook Inc gained between 0.4% and 1.3% and were among the biggest boosts to the S&P 500 and the Nasdaq.

Initial claims for state unemployment benefits fell 7,000 to 411,000 for the week ended June 19, the Labor Department said on Thursday, but were still higher than the 380,000 that economists had forecast.

The Commerce Department said the economy grew at a 6.4% rate last quarter, unrevised from the estimate published in May.

So far this month, the S&P 500 growth index has gained almost 4%, outperforming the value index's 2% drop.

The Dow Jones Industrial Average was up 1.04% at 34,225.35 points, while the S&P 500 gained 0.66% to 4,269.79.

The Nasdaq Composite added 0.72% to 14,374.56.

The S&P 500 technology, healthcare and communication services sector indexes hit record highs.

Eli Lilly and Co jumped almost 8% after the drugmaker said it would apply for the U.S. Food and Drug Administration's accelerated approval for its experimental Alzheimer's drug this year.

In response, Biogen Inc, which received a controversial approval for its Alzheimer's drug aducanumab earlier this month, dropped almost 6%.

MGM Resorts International rose 2.8% after Deutsche Bank upgraded the casino operator's stock to "buy" from "hold."

Accenture Plc gained 2% after the IT consulting firm raised its full-year revenue forecast.

Advancing issues outnumbered declining ones on the NYSE by a 2.34-to-1 ratio; on Nasdaq, a 2.19-to-1 ratio favored advancers.

The S&P 500 posted 33 new 52-week highs and 1 new lows; the Nasdaq Composite recorded 96 new highs and 22 new lows.

(Additional reporting by Devik Jain and Medha Singh in Bengaluru; Editing by Maju Samuel and Aurora Ellis)