Washington (CNN) As US officials were busy assessing Iran's missile attacks in Iraq late Tuesday, messages began arriving from Iran saying one thing: We're done.

Iran initiated contact through at least three back channels starting late Tuesday, including through Switzerland and other countries. There were "multiple messages and they were all the same," a person familiar with the matter said. Iran wanted to convey their retaliatory action had ended -- and was waiting to see how the US would respond.

The back-and-forth communication came as American officials were still determining the extent of the Iranian attacks, and were formulating plans for a response. In response, the US sought to communicate to Iran that its proxies in the region were of equal concern as the activities of the Iranian state, the person familiar said.

The National Security Council didn't respond to a request for comment.

Multiple administration officials previously told CNN there is a growing belief among some Trump administration officials that Iran's missiles intentionally missed areas populated by Americans when they targeted two Iraqi bases housing US troops early Wednesday local time. However, Army Gen. Mark Milley, the chairman of the Joint Chiefs of Staff, said it was his belief that Iran was trying to kill American military personnel in the attack.

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