This April 2012 satellite image provided by GeoEye appears to show a train of mining carts and other preparations underway at North Korea's Punggye-ri nuclear test site. (Associated Press)

Both companies provide satellite-based images that are used by the federal government and other clients to capture snapshots of the Earth from outer space. As the government looks to trim expenses, their business may be caught in the cross hairs.

In an open letter to GeoEye chief executive Matt O’Connell, DigitalGlobe executives said the proposed offer undervalues the company and contend that the firm remains better positioned to weather potential cuts to the federal budget.

The letter was signed by both DigitalGlobe chief executive Jeffrey Tarr and its chairman, Gen. Howell M. Estes III.

In a statement released Monday, O’Connell said the company was “disappointed” by DigitalGlobe’s decision to reject the offer and said that a merger of the two firms “makes clear strategic sense.”

“The combined company would be able to deliver significantly greater certainty in the continuity and quality of its future satellite constellation,” O’Connell said. “We view this proposal as being proactive to continue to deliver the high level of service to our government and commercial clients in the most cost effective manner.”

DigitalGlobe’s executives also wrote in the letter that the companies have been passing acquisition offers back and forth privately since Feb. 7.

At least one of those offers included a scenario in which DigitalGlobe’s shareholders would own 60 percent of a combined company while GeoEye’s shareholders would hold the remaining 40 percent. DigitalGlobe’s leadership would oversee the combined firm.

DigitalGlobe said in a statement on Sunday that it again put that offer on the table this weekend, but GeoEye rejected the proposal on both occasions.

For now, it seems any potential acquisition talks will set on hold. Tarr wrote in the letter that it is in the best interest of DigitalGlobe’s shareholders to “await the conclusion of the government budget decision process and to gain clarity with respect to EnhancedView funding.”

“When the government reaches its decision, DigitalGlobe will consider whether to make a proposal to acquire GeoEye,” Tarr continued.

The negotiations come as both companies prepare for prospective cuts to a $7.3 billion contract called EnhancedView that was awarded in 2010 to provide satellite imagery to the National Geospatial-Intelligence Agency.

While both firms have bulked up the commercial arm of their business in recent years, providing aerial-view images to industries as varied as those of natural gas and real estate, they continue to rely heavily on the federal government as a revenue source.

“We are realists, and we say as you look at the long-term prospects for the program, it’s going to be under some financial pressure,” O’Connell said in an interview Friday.

But DigitalGlobe remains bullish on the company’s prospects moving forward after confirming last week that it would receive full funding for its portion of EnhancedView through the end of September.

“Given the abruptness of your ‘public offer’ and our past discussions, we believe you made your hostile bid in desperation due to well-publicized concerns about potential government decisions that may jeopardize your portion of the EnhancedView program,” Tarr wrote of GeoEye in Sunday’s letter.

DigitalGlobe also reported last week that net income for the first quarter was $3.8 million, up from a net loss of $1.3 million during the same period last year.

“We are running the business for the long-term,” Tarr told investors last week. “We have not been notified of a cut [to EnhancedView]. We feel very confident in the value that we are delivering to our customer, and so we’re running our business with that as the basis.”