Jan 30 (Reuters) - Starbucks missed Wall Street estimates for the first quarter on Tuesday, in a sign that demand for its pricey coffees and cold drinks in the U.S. might be hitting a roadblock, while some of its international markets also faced a slowdown.

Shares of the company, however, rose 2% in extended trading, with analysts terming the overall results as "better than feared."

While Starbucks saw a strong start to the quarter with a 5.9% rise in traffic at its U.S. stores in October, the momentum quickly faded with November and December posting declines of 5.1% and 4.5%, respectively, brokerage Wells Fargo noted citing Placer.ai data.

"Investors probably must have expected worse and this is a better-than-feared situation where, while things aren't good, they're not as bad as they could have been," M Science analyst Matthew Goodman said.

Starbucks saw a "significant impact to traffic and sales" in the Middle East due to the Israel-Hamas war that broke out on Oct. 7, CEO Laxman Narasimhan said on a post-earnings call.

The war was also hurting traffic in the U.S., Narasimhan said, as consumers launched protests and boycott campaigns against the company over its stance on the conflict.

While comparable sales in China rose 10% in the quarter, improving from a 5% rise seen in the preceding three-month period, Starbucks said the recovery was still slower than its expectations.

The company's international segment posted only a 7% increase in same-store sales, missing analysts' estimate of 12.07% growth, driving global same-store sales growth of 5% below expectations of a 6.98% rise.

Per-share earnings of 90 cents also missed estimates of 93 cents, according to LSEG data.

"This is a little bit of a 'the bad news is out' kind of relief rally (in shares)," BTIG analyst Peter Saleh said.

(Reporting by Deborah Sophia in Bengaluru; Editing by Shilpi Majumdar)