AMSTERDAM, Oct 25 (Reuters) - Investor Cat Rock, one of the largest shareholders of online food ordering company Just Eat Takeaway.com, on Monday urged the company's management to consider the sale of its U.S. arm GrubHub.

Cat Rock, which holds a 6.5% stake in Takeaway, said selling or spinning off the unit would improve the valuation of Takeaway, which has lagged peers over the past year.

Amsterdam-based Takeaway, Europe's largest meals ordering company, only completed its $7.3 billion acquisition of GrubHub in June. Cat Rock did not call for the sale of GrubHub's significant Canadian and Australian operations.

"A deeply depressed stock price poses a real risk to [Takeaway's] business, limiting its financial and strategic flexibility, inviting competitors to invest in its markets, and leaving the company vulnerable to takeover bids well below its long-term intrinsic value," Cat Rock founder Alex Captain said in an open letter addressing company management.

Takeaway said in response that it had only acquired GrubHub four months ago. "While Grubhub has some specific challenges today it is a large and growing business with good underlying profitability," the company said.

At an Oct. 21 meeting with investors Takeaway CEO Jitse Groen outlined his strategy for defending market share in the U.S. by investing where the company is already strong, particularly in New York City where it is the biggest player.

Cat Rock's Captain, a long-time shareholder, argued that Grubhub's origins as a meal ordering platform left it at an logistical disadvantage to delivery-based competitors such as DoorDash and Uber. However Grubhub would be highly valuable to Amazon, Walmart or Instacart he said, and urged action by the end of this year.

Takeaway founder Groen, who is the company's second-largest shareholder with a 7.3% stake, told investors last week that he believed there would "over time inevitably be consolidation" in the U.S. delivery market and Grubhub would participate.

In a note analysts at Credit Suisse agreed with Cat Rock that a sale "could add value" but a sale by year end would be a difficult timeline to meet.

(Reporting by Toby Sterling; Editing by Kirsten Donovan)