Apple's (AAPL) fiscal first quarter results showed a bit of stabilization in China and "record revenues" in India, according to CEO Tim Cook, but the U.S. technology giant still faces challenges in these emerging but increasingly "critical" markets.

Greater China revenues were down 12 percent year-on-year to $16.2 billion, marking another double-digit decline in the region for Apple. The bright spot however was that Greater China revenues – which includes Mainland China, Taiwan and Hong Kong – were up 85 percent on the quarter, thanks to the iPhone 7 series. And Cook said on an earnings call that on a "constant currency" basis, sales in mainland China were up six percent.

It points to some stabilization, according to analysts.

"Improvement with Greater China revenue -8 percent in constant currency and Mainland China +6 percent suggests the issues are more cyclical than secular. The Greater China decline should be similar in F2Q (fiscal second quarter), so improvement and possibly some growth come in the F2H (fiscal second half)," UBS said in a note on Wednesday.

Cook said that he does not expect next quarter's performance to be "dramatically different" to the first fiscal quarter, offering little in the way of specific numbers.

And in India – a country Cook has touted the potential of on many occasions – Apple recorded "record revenue". The Cupertino, CA-based firm does not break out specific figures for India. And Apple does not look like pulling back from the country.

"We are in discussions on a number of things, including retail stores, and fully intend to invest significantly in the country and believe it's a great place to be," Cook said on the earnings call.

China key for iPhone 8 win

But some analysts have struck a note of caution on Apple's chances in China – a notoriously brutal market. Take Xiaomi as an example . The Chinese smartphone maker, which was once the darling of the market and growing at a quick pace, saw shipments decline last year 22 percent, according to Counterpoint Research.

Last year, Apple's iPhone failed to clinch the title for the top selling smartphone in China for the first time since 2012, Counterpoint said. Apple has struggled to compete against newer players such as Oppo which grew 109 percent in terms of shipments last year, and Vivo which was up 78 percent. Huawei in the premium end of the market has also made great strides in China.

A lot is riding on Apple solidifying its business in China and returning it to growth.

"We consider a return to growth in China critical to a successful iPhone 8 cycle," UBS said. The iPhone 8 is rumored to be a special anniversary edition phone with major upgrades.

"I think right now it really comes down to can you see China growth start to see a renaissance … especially going into iPhone 8 … It all comes down to China is key fuel in the growth engine for Apple," Daniel Ives, who leads global investor relations for Synchronoss, told CNBC on Wednesday.

Long-term play on India

While Cook spoke of the India boost, Ives called this a "nascent" market, and like China, it's a market where the iPhone is out of the price range of many consumers, and where there are many competitors.

In India, Apple sold 2.5 million iPhones last year, up from 2 million the year before, according to Neil Shah, an analyst at Counterpoint Research. This is small compared to the near 50 million units it sold in China in 2016.

Apple will find it difficult in the near term to grow share dramatically, Shah said, as 75 percent of smartphones sold in the country are below $150, a segment Apple doesn't play in. But if Apple lays the right groundwork, as Cook has suggested, it could be a long-term bet for the world's most valuable company.

"They have to invest a lot in these markets, build the brand, build the channels, so when the market matures those consumers are looking at Apple," Shah told CNBC by phone.