(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window.) * 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 up: Dow 0.67%, S&P 0.54%, Nasdaq 0.85% (Adds comment, details; updates prices) June 24 (Reuters) - The Nasdaq and the S&P 500 indexes hit all-time highs on Thursday, boosted by shares of Tesla and other top-shelf technology firms as data showing fewer weekly jobless claims bolstered views of a steady recovery in the labor market. Focus was also on President Joe Biden’s meeting with a bipartisan group of U.S. senators at 11:45 a.m. ET to discuss their proposed framework for a spending bill to invest in the country’s bridges, roads and other physical infrastructure. “Washington needs to get something done,” said Michael Sheldon, chief investment officer of RDM Financial Group at Hightower. “If (Biden) can get a trillion dollar or somewhat above a trillion dollar deal, there’s a decent chance that he may accept that in order to move forward and achieve some of his goals.” After the U.S. economy grew at a 6.4% annualized rate in the first quarter, thanks to the massive fiscal stimulus, all eyes are on the infrastructure deal that could steer the next leg of the recovery for the world’s largest economy. Tesla Inc rose 5.8% 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-cap tech names such as Apple Inc, Microsoft Corp, Google-owner Alphabet Inc, Netflix Inc and Facebook Inc also gained between 0.2% and 0.9% and were among the biggest boosts to the S&P 500 and the Nasdaq. “Investors have realized that many of these stocks were not that highly priced in the case of very large cap technology companies,” Sheldon said. 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. So far this month, the value index, which includes economy-linked energy, financial and industrial stocks, is lagging its tech-heavy growth counterpart despite maintaining a strong lead year-to-date. At 11:29 a.m. ET, the Dow Jones Industrial Average was up 228.42 points, or 0.67%, at 34,102.66, and the S&P 500 was up 22.71 points, or 0.54%, at 4,264.55. The Nasdaq Composite was up 121.38 points, or 0.85%, at 14,393.11. Technology, healthcare and communication services sector indexes were at their peaks. Eli Lilly and Co jumped 6.5% 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 6%. MGM Resorts International rose 4.1% 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 decliners by a 1.8-to-1 ratio on the NYSE and by a 1.9-to-1 ratio on the Nasdaq. The S&P 500 posted 31 new 52-week highs and one new low, while the Nasdaq recorded 129 new highs and 23 new lows. Reporting by Devik Jain and Medha Singh in Bengaluru; Editing by Maju Samuel Our Standards: The Thomson Reuters Trust Principles.