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* Iran fires rockets overnight at Iraqi bases housing U.S. forces
* Trump comments fuel rally in risk assets
* Walgreens Boots slides on quarterly profit miss
* Indexes up: Dow 0.9%, S&P 0.9%, Nasdaq 1.0% (Updates to late afternoon)
By Caroline Valetkevitch
NEW YORK, Jan 8 (Reuters) - U.S. stocks climbed on Wednesday, with the S&P 500 and the Nasdaq hitting record highs, after President Donald Trump's comments eased fears of an all-out conflict in the Middle East.
Trump's comments at a White House briefing followed Iran's missile strikes overnight on military bases housing U.S. troops in Iraq.
The U.S. president said the strikes had not harmed any Americans and that Tehran appeared to be standing down.
Comments earlier from Iran's foreign minister that the country did not seek an escalation and a tweet from Trump that "All is well!" also helped to calm investor jitters.
Stocks were edging higher before Trump's comments, but he confirmed the view that the United States was "willing to make peace with anyone who wants to," said Michael O'Rourke, chief market strategist at JonesTrading in Stamford, Connecticut.
"His tone was very conciliatory, so I think everyone views this as a de-escalation, and the S&P pushed to new all-time highs."
Global markets have been rattled by concerns about rising tensions in the Middle East after the U.S. killing of influential Iranian Major General Qassem Soleimani on Jan. 3.
The S&P 500 energy index was trading more than 1% lower, while the rest of the S&P sectors were trading higher.
The Dow Jones Industrial Average rose 261.69 points, or 0.92%, to 28,845.37, the S&P 500 gained 27.81 points, or 0.86%, to 3,264.99 and the Nasdaq Composite added 93.65 points, or 1.03%, to 9,162.23.
Among the day's decliners, Boeing fell 1.1% after a 737-800 jet made by the company and belonging to a Ukrainian airline burst into flames shortly after takeoff from Tehran, killing all 176 people aboard.
Also, Walgreens Boots Alliance Inc slid 5.7% as its quarterly profit missed expectations. Shares in rival CVS Health fell 1.5%.
Meanwhile, Lennar Corp gained 1.8% after the No. 2 U.S. homebuilder beat quarterly profit estimates on lower home prices and mortgage rates.
Adding to the upbeat mood, the ADP National Employment Report showed private payrolls jumped by 202,000 jobs last month, much above the 160,000 rise expected by economists polled by Reuters.
Advancing issues outnumbered declining ones on the NYSE by a 1.77-to-1 ratio; on Nasdaq, a 1.82-to-1 ratio favored advancers.
The S&P 500 posted 58 new 52-week highs and no new lows; the Nasdaq Composite recorded 106 new highs and nine new lows. (Additional reporting by Sruthi Shankar and Susan Mathew in Bengaluru; Editing by Shounak Dasgupta and Jonathan Oatis)