MOSCOW — President Vladimir V. Putin on Monday approved the delivery of a sophisticated air defense missile system to Iran, potentially complicating negotiations on Tehran’s nuclear program and further straining ties with Washington.

The sale could also undermine the Obama administration’s efforts to sell Congress and foreign allies on the nuclear deal, which Iran and the United States are still struggling to complete. It might also reduce the United States’ leverage in the talks by making it much harder for the United States or Israel to mount airstrikes against Iran’s nuclear infrastructure if the country ignored such an agreement.

“It is significant as it complicates the calculus for planning any military option involving airstrikes,” said David A. Deptula, a retired three-star general who served as the Air Force’s deputy chief of staff for intelligence, surveillance and reconnaissance.

The deal, worth an estimated $800 million to Russia, also reinforced Israeli and Arab fears that a nuclear pact and the subsequent lifting of sanctions would ignite the Iranian economy, making it a more formidable regional power.