WASHINGTON (Reuters) -A Chicago-based private equity firm - controlled by a member of the family that founded American publishing company Rand McNally - has an "economic interest" in the logistics company involved in a controversial new aid distribution operation in Gaza.

McNally Capital, founded in 2008 by Ward McNally, helped "support the establishment" of Safe Reach Solutions, a McNally Capital spokesperson told Reuters. SRS is a for-profit company established in Wyoming in November, state incorporation records show. 

It is in the spotlight for its involvement with the U.S.- and Israeli-backed Gaza Humanitarian Foundation, which last week started distributing aid in the war-torn Palestinian enclave. The foundation paused work on Wednesday after a series of deadly shootings near the distribution sites of people on their way to pick up aid. It has suffered from the departure of senior personnel. 

"McNally Capital has provided administrative advice to SRS and worked in collaboration with multiple parties to enable SRS to carry out its mission," the spokesperson said. "While McNally Capital has an economic interest in SRS, the firm does not actively manage SRS or have a day-to-day operating role."

SRS is run by a former CIA official named Phil Reilly, but its ownership has not previously been disclosed. Reuters has not been able to establish who funds the newly created foundation.

The spokesperson did not provide details of the scale of the investment in SRS by McNally Capital, which says it has $380 million under management.

McNally Capital founder Ward McNally is the great great great grandson of the co-founder of Rand McNally. The McNally family sold the publishing company in 1997. 

A spokesperson for SRS confirmed it worked with the foundation, also known as GHF, but did not answer specific questions about ownership.

GHF, which resumed aid distribution on Thursday, did not respond to a request for comment

While Israel and the United States have both said they don't finance the operation, they have pushed the United Nations and international aid groups to work with it, arguing that aid distributed by a long-established U.N. aid network was diverted to Hamas. Hamas has denied that.

Israel blocked almost all aid into Gaza for 11 weeks until May 19, and has since only allowed limited deliveries in, mostly managed by the new GHF operation. 

This week GHF pressed Israel to boost civilian safety beyond the perimeter of its distribution sites after Gazan health officials said at least 27 Palestinians were killed and dozens wounded by Israeli fire near one of the food distribution sites on Tuesday, the third consecutive day of chaos and bloodshed to blight the aid operation.

The Israeli military said its forces on Tuesday had opened fire on a group of people they viewed as a threat after they left a designated access route near the distribution center in Rafah. It said it was investigating what had happened.

The U.N and most other aid groups have refused to work with GHF because they say it is not neutral and that the distribution model militarizes aid and forces displacement. 

SRS subcontracts with U.S. private security firm UG Solutions, which provides armed U.S. military veterans to guard the distribution sites and transportation of the aid, two sources familiar with the operations said. UG Solutions did not respond to a request for comment. 

The SRS spokesperson said in a statement that under Reilly's leadership, "SRS brings together a multidisciplinary team of experts in security, supply chain management, and humanitarian affairs."

McNally Capital has investments in defense contracting companies. Among the firms it acquired was Orbis Operations, a firm that specializes in hiring former CIA officers. Orbis did not return calls for comment. Reilly used to work for Orbis.