NEW YORK — When Marc Caira joins Tim Hortons Inc. in early July as president and chief executive officer, one of his first tasks will be looking at every avenue to grow the company’s brand in the United States, a market the Toronto-based restaurant chain has been expanding methodically in since its entry nearly 30 years ago, said Paul House, executive chairman, president and c.e.o.

“We think we’re now at that critical point that we’ve got a base of business, we’ve got a reputation that’s been established and not to the extent that we’d like to have it, but I think it’s going to give us permission to do things that we couldn’t have done five years ago,” Mr. House said in a June 4 presentation at the Goldman Sachs Lodging, Gaming, Restaurant and Leisure Conference in New York. Mr. House will transition into a new role as non-executive chairman when Mr. Caira takes over in July.

Mr. House said Tim Hortons has built a growing regional presence in the Northeast and Midwest of the United States, and now has restaurants in 11 different states. In total, Tim Hortons operates more than 800 restaurants in the United States. More recently, he said the company has deployed capital into its highest-growth U.S. markets “to increase the density of our restaurant footprint.”

“Higher density allows us to leverage our advertising scale, it enables guests to visit more frequently and it creates opportunity for increased average unit volumes,” Mr. House said.

Mr. House said system-wide sales progress in the United States has pleased Tim Hortons, and the company has several high-volume restaurants in its major markets. The company just does not have enough of them, he said.

“The growth pattern we see in the U.S. is no different than we saw in our early years of development markets in Canada,” he explained. “As we develop those markets we reach the density and sales volume necessary to generate stronger returns. Nevertheless, we believe there are opportunities to drive better returns in the U.S. market, potentially including through a less capital intense development approach.”

That approach may include working with well-capitalized franchisees that have the resources to develop and operate multiple locations, he said.

“Working with such franchisees would enable us to deploy less capital, while enhancing development and brand awareness in various markets,” he said. “This is an approach we are actively considering to complement our existing development efforts in conjunction with our ongoing review of how we develop the market.

“We are committed to the U.S. market and we continue to believe it holds great potential for us. However, we believe we can and should be achieving improved returns. We remain open to additional avenues to further build and develop the brand in the United States.”

The first U.S. Tim Hortons location opened in Amherst, N.Y., in 1985. The 500th location opened in Detroit in 2008. Tim Hortons restaurants are located in 11 states: Delaware, Indiana, Kentucky, Maine, Maryland, Michigan, New York, Ohio, Pennsylvania, Virginia and West Virginia. New York state has the most locations, with more than 200.

The restaurant chain offers 63 varieties of donuts, more than 15 varieties of muffins, 10 types of cookies and 12 varieties of bagels as well as oatmeal, Danishes, croissants, fruit smoothies, yogurt and berries, hot breakfast sandwiches, flatbread breakfast Paninis, soups, chili and coffee.