Oct 26 (Reuters) - Visa Inc"s (V.N) quarterly profit topped Wall Street expectations on Tuesday, as a recovery in travel and an improving global economic picture drove volume growth at the world"s largest payment processor. But cross-border travel was still well below pre-pandemic levels, Visa said, with regions such as the Asia Pacific remaining closed. "Our business has been on a recovery track for the past three to four quarters. However, we are not back to normal yet globally," Chief Financial Officer Vasant Prabhu told analysts on a call. "The timing of reopening in key countries across Asia, both domestically and for cross-border travel is a key variable." In a sign of resilience, however, debit and e-commerce activity outperformed in the quarter even as in-store shopping picked up and credit card volumes recovered. Visa"s net income rose to $1.65 per Class A share for the fourth quarter ended Sept. 30, beating analysts" estimate of $1.54 per share, according to Refinitiv data. In the United States, reopening economies have fueled widespread demand for travel and shopping from consumers stuck indoors for more than 18 months. U.S. to Mexico travel remained robust, Visa said. read more The company forecast fiscal 2022 first-quarter net revenue growth in the high teens, while total cross-border volume in the reported quarter rose 38% on a constant dollar basis from a year earlier. Talking about its assumptions for internal planning purposes, Visa said it assumes the recovery in cross-border travel to continue through fiscal 2022 and reach 2019 levels in the summer of 2023. Total payment volumes rose 17% on a constant dollar basis from a year earlier, while the number of transactions processed by Visa rose 21% to 45.3 billion. American Express"s (AXP.N) profit also topped estimates last week, as higher usage of its cards fueled a strong recovery in overall spending.