July 23 (Reuters) - Oilfield services giant Schlumberger NV (SLB.N) issued a bullish forecast for 2021 on Friday as second-quarter profit topped estimates due to surging margins, with a rebound in oil prices boosting demand for its software and equipment. Energy services firms are benefiting from a resumption of drilling driven by rising crude prices, which are up 18% in the latest quarter and 42% since the start of 2021. Still, oilfield activity levels remain far below pre-pandemic levels and oil demand could face a threat as a resurgence of infections from coronavirus variants prompts fresh restrictions in some parts of the world. Schlumberger officials offered an optimistic outlook for the rest of the year, and said they expect further growth and margin expansion in the company"s North American and international operations. International revenue could rise at a double-digit percentage rate compared with year-ago levels, officials said. Its North American business, which fell 1% versus a year ago, could "surprise to the upside" due to spending by private operators, Chief Executive Olivier Le Peuch said. "Industry projections of oil demand reflect the anticipation of a wider vaccine-enabled recovery, improving road mobility, and the impact of various economic stimulus programs," Le Peuch said, cautioning the COVID-19 pandemic continues to threaten the demand recovery. U.S. oil output may not reach pre-pandemic levels until after 2022, Le Peuch said, adding that international supply and demand conditions would push oil and gas activity beyond 2019 levels in the next two to three years. Rival Halliburton this week also delivered a bullish outlook for the oil industry recovery, while Baker Hughes missed earnings expectations following a hit from restructuring charges. read more Schlumberger reported net income of $431 million, or 30 cents per share, for the three months to June 30, compared with $299 million, or 21 cents per share, in the first quarter. Wall Street analysts had anticipated earnings of 26 cents per share, according to Refinitiv IBES. Operating margins nearly doubled to 14.3%, the highest since 2018, led by big gains in its software and reservoir performance units. Those gains, which marked the fourth consecutive quarter of margin expansion, reflected past cost-cutting and big year-over-year software revenue increases. Analysts for investment firm Tudor Pickering Holt & Co said the results were strong, but lamented that Schlumberger"s stock - along with other oilfield companies - had continued to underperform. Shares were up a fraction in early trading at $28.08. They are up about 28% year-to-date, trailing the jump in oil prices.