* Nasdaq set for best weekly winning streak since Jan 2020

* Data shows jobless rate at 3.7% in May; wage growth moderates

* Amazon up on report of its talks for low-cost mobile services

* Materials, industrials lead S&P sectoral gains

* Indices up: Dow 2.11%, S&P 500 1.46%, Nasdaq 1.01%

June 2 (Reuters) - U.S. stocks rallied on Friday after a labor market report showing moderating wage growth in May, indicating the Federal Reserve may skip a rate hike in two weeks, while markets welcomed a Washington deal that avoided a catastrophic debt default.

The tech-heavy Nasdaq index hit a 13-month intraday high as it headed for a sixth-straight week of gains that would mark its best winning streak since January 2020.

U.S. job growth accelerated in May but a surge in the unemployment rate to a seven-month high of 3.7% suggested labor market conditions were easing, the Labor Department said.

The jump in the unemployment rate from a 53-year low of 3.4% in April reflected a drop in household employment and a rise in the overall workforce. A bigger labor pool is easing pressure on businesses to raise wages and helping decelerate inflation.

"While it appears to be a hot number on the actual number of people employed, the wage rate is not increasing as fast," said Kim Forrest, chief investment officer at Bokeh Capital Partners in Pittsburgh. "That is a softening effect and is this the mythical soft landing? Looks like that."

The data brought relief to investors who mostly expect the Fed to pause hiking rates at its policy meeting on June 13-14. It would be the first halt since the Fed started its aggressive anti-inflation policy tightening more than a year ago.

But some pointed to the much hotter-than-expected jobs data as a sign the Fed still has not yet tamed inflation.

"Our view is and has been that the market is completely wrong on assessing what the Federal Reserve is doing," said Phil Orlando, chief equity strategist at Federated Hermes in New York.

"The market's perception is that this economy was going to cool, inflation was going to collapse and the Fed was going to turn around and start cutting interest rates. That's wrong."

Fed funds futures showed a 66.6% probability that the Fed will hold rates steady in two weeks, down from 79.6% on Thursday, according to CME Group's FedWatch Tool.

Markets now await data on key consumer prices a day before the Fed's rate decision.

Also lifting an investor headwind was the Senate passing a bill late on Thursday to lift the government's $31.4 trillion debt ceiling, avoiding what would have been a catastrophic, first-ever default.

Wall Street's fear gauge, the CBOE volatility index fell to its lowest since November 2021, down 1 point at 14.3 points.

The Dow Jones Industrial Average rose 701.39 points, or 2.12%, to 33,762.96, the S&P 500 gained 61.71 points, or 1.46%, to 4,282.73 and the Nasdaq Composite added 130.52 points, or 1%, to 13,231.50.

Amazon.com Inc gained 1.6% after a report that the company is in talks with telecom operators to offer low-cost mobile services in the United States.

All 11 major S&P 500 sectors traded higher, with the materials index jumping 3.3% and the consumer discretionary sector, housing Amazon, rising 2.4%.

Advancing issues outnumbered declining ones on the NYSE by a 5.03-to-1 ratio; on Nasdaq, a 2.50-to-1 ratio favored advancers.

The S&P 500 posted 15 new 52-week highs and two new lows; the Nasdaq Composite recorded 66 new highs and 34 new lows.

(Reporting by Herbert Lash, additional reporting by Shreyashi Sanyal, Shristi Achar A and Shashwat Chauhan, in Bengaluru; Editing by Nivedita Bhattacharjee and Maju Samuel)