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Tehran proposed ending support for Lebanese and Palestinian militant groups and helping to stabilise Iraq following the US-led invasion.
Offers, including making its nuclear programme more transparent, were conditional on the US ending hostility.
But Vice-President Dick Cheney's office rejected the plan, the official said.
The offers came in a letter, seen by Newsnight, which was unsigned but which the US state department apparently believed to have been approved by the highest authorities.
In return for its concessions, Tehran asked Washington to end its hostility, to end sanctions, and to disband the Iranian rebel group the Mujahedeen-e-Khalq and repatriate its members.
Former Iraqi leader Saddam Hussein had allowed the rebel group to base itself in Iraq, putting it under US power after the invasion.
One of the then Secretary of State Colin Powell's top aides told the BBC the state department was keen on the plan - but was over-ruled.
"We thought it was a very propitious moment to do that," Lawrence Wilkerson told Newsnight.
"But as soon as it got to the White House, and as soon as it got to the Vice-President's office, the old mantra of 'We don't talk to evil'... reasserted itself."
Observers say the Iranian offer as outlined nearly four years ago corresponds pretty closely to what Washington is demanding from Tehran now.
Since that time, Lebanese guerrilla group Hezbollah inflicted significant military losses on the major US ally in the region, Israel, in the 2006 conflict and is now claiming increased political power in Lebanon.
Palestinian militant group Hamas won power in parliamentary elections a year ago, opening a new chapter of conflict in Gaza and the West Bank.
The UN Security Council has imposed sanctions on Iran following its refusal to suspend its uranium enrichment programme.
Iran denies US accusations that its nuclear programme is designed to produce weapons.
“Lord our Father, our young patriots, idols of our hearts, go forth into battle — be Thou near them! With them — in spirit — we also go forth from the sweet peace of our beloved firesides to smite the foe.
O Lord our God, help us tear their soldiers to bloody shreds with our shells; help us to cover their smiling fields with the pale forms of their patriot dead; help us to drown the thunder of the guns with the shrieks of their wounded, writhing in pain; help us to lay waste their humble homes with a hurricane of fire; help us to wring the hearts of their unoffending widows with unavailing grief; help us to turn them out roofless with their little children to wander unfriended in the wastes of their desolated land in rags and hunger and thirst, sports of the sun flames in summer and the icy winds of winter, broken in spirit, worn with travail, imploring thee for the refuge of the grave and denied it —
For our sakes who adore Thee, Lord, blast their hopes, blight their lives, protract their bitter pilgrimage, make heavy their steps, water their way with their tears, stain the white snow with the blood of their wounded feet!
We ask it, in the spirit of love, of Him Who is the Source of Love, and who is the ever-faithful refuge and friend of all that are sore beset and seek His aid with humble and contrite hearts. Amen.
Mark Twain