The newly announced Iran nuclear deal and the negotiations leading up to it already are fueling an all-but-declared nuclear arms race in the Middle East, according to current and former government officials who say the situation also creates an opening for Russia to exert more influence in the region.

"We have given Iran the path it has been seeking for almost 35 years. The other states in the region are not going to sit idly by, which is why in effect the nuclear arms race is already underway," former U.N. Ambassador and Fox News contributor John Bolton said, adding that Iran and other nations have used civilian nuclear energy programs as cover for covert enrichment programs.

The Obama administration announced the deal along with other world powers early Tuesday morning. The terms call for suspending and curbing components of Iran's nuclear program in exchange for valuable sanctions relief.

But in the last six months, Russia has struck three significant nuclear deals with long-time U.S. Middle East allies, effectively capitalizing on regional distrust of Iran.

In February, a deal was sealed with the Egyptian government of President Abdel Fattah el-Sisi to help Cairo build and operate its first nuclear reactor. A month later, in March, Jordan signed a $10 billion deal with Russia to build the kingdom's first nuclear power plant, with two 1,000-megawatt reactors in the country's north. And in June, Saudi Arabia and Russia agreed to a deal, the terms of which are not public. But unnamed sources told the Al Arabiya TV network that the kingdom planned to build 16 nuclear reactors that Russia would play a significant role in operating.

"Every Sunni Arab nation is going to see [a nuclear Iran] as an inevitable outcome," Republican presidential candidate and Sen. Lindsey Graham, R-S.C., said. "The worst possible outcome of the deal would be to create a nuclear arms race in the Mideast where Sunni Arabs feel threatened."

Republican Sen. Ben Sasse, of Nebraska, said in a statement, "Sadly, the Administration just lit the fuse for a nuclear arms race in the Middle East. We all know Iran's neighbors will not sit idly as the world's largest state-sponsor of terror becomes a nuclear-threshold state."

A seasoned intelligence official who recently returned from the region said private discussions revealed that allies, including Egypt and Saudi Arabia, felt abandoned by the U.S. as the administration seemed to put securing a deal with Tehran ahead of the long-time alliances.

"The race is on, and the U.S. has got to get in the driver's seat," the intelligence official said of a regional arms race. "The administration has created a major void, allowing an opening for Russia."

Putin, who analysts say stands to gain the most from a newly empowered Iran, hailed the deal as a tremendous accomplishment, and said in a statement, "We expect that all the parties concerned, primarily the six states involved in the negotiations, will comply with the deal in full. ... Our bilateral relations with Iran will receive a new impetus and will no longer be influenced by external factors."

On Monday, White House spokesman Josh Earnest said the administration's strategy was designed to achieve the opposite effect, to minimize the likelihood of a nuclear arms race.

"One of the reasons we have sought to pursue diplomatic opportunities to prevent Iran from obtaining a nuclear weapon is the risk that exists that if Iran does obtain a nuclear weapon, it could set off a nuclear arms race in the most volatile region of the world," Earnest said in a response to a question about Saudi Arabia's intentions if no agreement was reached. "That would be destabilizing to an already volatile region of the world. It also would have a negative impact on the national security interests of the United States. It obviously would not be good for our closest ally in the region, Israel."