The Congress should, for now, appoint an interim president and four working presidents or vice presidents, the 88-year-old suggested in a statement on Monday.
The decisions should be taken at a Congress Working Committee meeting to be chaired by former prime minister Manmohan Singh, Karan Singh suggested.
According to his plan, the vice presidents could be each in charge of a zone, north, south, east or west. "This will enable the introduction of younger people into positions of authority," said the Congress leader.
Karan Singh said as someone who had joined the Congress in 1967, over half a century ago, he was "aghast to see the confusion and disorientation..." since Rahul Gandhi resigned on May 25.
"Instead of honouring his bold decision, a month was wasted in pleading with him to take back his resignation which, as a man of honour and integrity, he should not have been pressurized to do so," he said, noting that six weeks on, there was still no alternative structure in place.
Karan Singh's letter surfaced as Mukul Wasnik and Mallikarjun Kharge emerged as front runners for Congress president's post. Sources say the Congress is weighing the possibility of three young vice presidents like Sachin Pilot, Jyotiraditya Scindia and Milind Deora.
The Congress Working Committee, the highest decision-making body of the party, is expected to meet this week to take a call.
Rahul Gandhi last week posted what could best be described as a public resignation letter, making it clear that he was firm on quitting as Congress president for the sake of accountability, after the party's national election defeat.
The 49-year-old had resigned much earlier, on May 25, days after the Congress finished with 52 seats in the national election, pulverized by Prime Minister Narendra Modi's BJP which won a giant mandate to remain in power.
For weeks, several Congress leaders have pleaded with Rahul Gandhi to change his mind, without luck.