The South Korean giant delivered 77 million smartphones in the quarter, up 5.5 percent from a year ago, for a market share of 22.4 percent, research firm IDC said.
That compared with a 15 percent drop in sales for Apple's iPhones, which accounted for 11.8 percent, IDC said.
A separate survey by Strategy Analytics had a similar estimate, with Samsung at 22.8 percent to 11.9 percent for Apple.
Neil Mawston, executive director at Strategy Analytics, said he sees Samsung making further gains this year.
"With a new Galaxy Note 7 flagship model rumored to be on the way, Samsung will be able to strengthen its smartphone leadership into the second half of the year," Mawston said.
"Apple continues to face iPhone fatigue among consumers and the new iPhone SE model has not been able to stem that trend."
IDC's Ryan Reith said the saturation of many markets has forced makers to rethink their strategy. "Apple is beginning to put more emphasis on 'device as a service' to try to prevent lengthening replacement cycles," he said.
"This is a growing theme we have heard more about from PCs to smartphones. Additionally, the overall China market slowdown continues to ramp up competition in other high growth markets like India, Indonesia, and Middle East."
Both surveys showed China's Huawei the number three vendor with a 9.4 percent market share.
Other Chinese vendors were in the top five.
The Strategy Analytics report showed Oppo with 5.3 percent and Xiaomi fifth with 4.3 percent.
IDC said overall smartphone sales rose 0.3 percent to 343.3 million units, while the second survey showed a one percent rise to 340 million.