The nearly $7 billion U.S lunch meat market grew by 18% in the 8 weeks to June 13, but Oscar Mayer sales rose only 9%, according to Nielsen data analyzed by Wells Fargo. Meanwhile, sales of rival brands like Hormel Foods' Applegate and Tyson Foods' Hillshire surged 37% and 27%, respectively.

Cheese and chilled processed meat are Kraft Heinz's top two U.S. businesses by retail sales, but Euromonitor data shows Kraft Heinz's market share in both categories has steadily shrunk since 2015. The company is due to report quarterly earnings on Thursday.

To fuel growth, Kraft Heinz needs to innovate, a process that could take several years, analysts said.

"The higher priced brands are seeing the strongest growth. People aren't trading down to private-label, they're buying the quality stuff," Wells Fargo analyst John Baumgartner said. "Oscar Mayer doesn't have that quality perception with consumers - they're going to have to launch a product that's really clean-label so they can charge more."

To appeal to environmentally conscious consumers, the labels of Applegate's roughly $16-a-pound hams say prominently that its pigs are "humanely raised" and given vegetarian feed on family farms. The packaging of Oscar Mayer products, which cost about $4.85 per pound in stores, say they don't contain hormones, nitrates or artificial ingredients - a years-old declaration in the industry.

While Hillshire has rolled out cheese and cracker snack plates with premium prosciutto and wine-infused salami, Oscar Mayer's cheaper plates come with hickory-smoked ham and hard salami.

Kraft Heinz CEO Miguel Patricio, who began revamping operations when he took over about a year ago, said in April the company had postponed a lot of innovation this year to spend more on media and reduce the number of products it makes. Kraft Heinz declined to comment for this story.

The company's U.S. cheese sales rose 24% in the 8 weeks to June 13, the Nielsen data shows, once more lagging rivals - including premium private-label brands - that drove 32% growth in the $19 billion U.S. packaged cheese market.

Kraft Heinz has taken some steps to innovate. In September, a fund backed by the company led a $3.5 million investment in animal-free dairy cheese startup New Culture. Kraft Heinz's Cracker Barrel cheddar cheese is considered premium and has seen some innovation, but it was launched in 1954 and analysts say it needs to further revamp its portfolio through tie-ups with specialty cheese-makers or regional dairies.

By Richa Naidu