"It is very important to preserve it in its current form and of course the participation of the United States will be a very significant factor in this regard," Lavrov told reporters on a visit to Kazakhstan.
Under the deal, Iran agreed to restrict its nuclear programme in return for lifting most international sanctions that had crippled its economy.
Trump is expected to announce soon that he will decertify the deal, a senior White House official said on Thursday, in a step that potentially could cause the 2015 accord to unravel.
Trump, who has called the pact an "embarrassment" and "the worst deal ever negotiated", has been weighing whether it serves US security interests as he faces an October 15 deadline for certifying that Iran is complying with its terms.
If Trump declines to certify Iran's compliance, US congressional leaders would have 60 days to decide whether to reimpose sanctions on Tehran suspended under the agreement.
(Reporting by Raushan Nurshayeva; Writing by Olzhas Auyezov; Editing by Maria Kiselyova and Alison Williams)