They call for fewer concessions on international nuclear inspections and on research and development activities.
The publication of the letter comes as the deadline for a final accord nears.
US Secretary of State John Kerry and his Iranian counterpart Mohammad Javad Zarif are to fly to the Austrian capital Vienna on Friday to join the negotiations, which may need to continue beyond 30 June.
The so-called P5+1 - the US, UK, France, China and Russia plus Germany - wants to limit Iran's sensitive nuclear activities to ensure that it could not build a nuclear weapon quickly.
Iran, which wants sanctions lifted in exchange, insists its nuclear work is peaceful.
'Tracks with US position'
The open letter published by the Washington Institute for Near East Policy on Thursday is signed by a bipartisan group of US diplomats, legislators, policymakers and experts who have met regularly over the past three years to discuss Iran.
"Most of us would have preferred a stronger agreement," the letter says.
"The agreement will not prevent Iran from having a nuclear weapons capability. It will not require the dismantling of Iran's nuclear infrastructure," it adds.
"It will however reduce that infrastructure for the next 10 to 15 years. And it will impose a transparency, inspection, and consequences regime with the goal of deterring and dissuading Iran from actually building a nuclear weapon."
The letter calls on Mr Obama to insist that Iran provide information about nuclear weapons research Western powers suspect it has carried out, and allow inspectors from the International Atomic Energy Agency (IAEA) access to military sites.
The president is also urged to establish strict limits on the research and development of centrifuges used to enrich uranium to preclude the "rapid technical upgrade and expansion" of Iran's enrichment capacity at the end of any deal. Enriched uranium can be used to make fuel for both nuclear energy and weapons.
A senior Obama administration official said it had received the letter and that it "in large part tacks with the US negotiating position inside the negotiating room".