Stock markets in Asia have already given investors most of the returns they can get this year — and shares prices in the region may struggle to grow much more for the rest of 2019, J.P. Morgan said on Tuesday.

Asian stocks have had a strong start to the year after ending 2018 in negative territory. The MSCI Asia ex-Japan index — a widely followed benchmark for stocks in the region — has grown by around 13.68 percent so far this year. The index fell by 16.24 percent last year.

"We've been a bit more on the cautious side since ... the second week of March," Mixo Das, Asia equity strategist at J.P. Morgan, told CNBC's "Squawk Box."

"I think most of the gains for this year in Chinese as well as Asian equity markets are already behind us. From here, it's going to be more of a difficult slog. We still see gains but it's going to be a much more volatile process," he added.

Asked how Asian share prices will likely perform between now till the end of the year, Das responded that they could grow by a low single-digit, or remain largely flat.

He explained that valuations have become stretched compared to projections on where earnings are headed in the coming months. In addition, he said sentiment among investors have become "overextended" and "overheated."