(Reuters) - Shares of former U.S. President Donald Trump's media company surged 6% on Tuesday to their highest since June in one of the heaviest trading sessions since the Truth Social platform's Wall Street debut in March.

Trump Media & Technology Group's ( DJT ) leap to $31.55 a share added to recent strong gains reflecting betting odds that show Trump with an edge over Democratic candidate Vice President Kamala Harris in a neck-and-neck race for the White House.

About $2 billion worth of shares of Trump Media ( DJT ) had been exchanged as of mid-afternoon, according to LSEG data. That put the stock on track for its third busiest trading session since Trump Media's ( DJT ) market debut in March. 

Since its listing, Trump Media ( DJT ) has been popular with traders viewing it as a speculative bet that the former president will win the Nov. 5 presidential election.

Turnover in Trump Media ( DJT ) hit $3.4 billion on July 15 after a would-be assassin shot Republican candidate Trump in the ear at a campaign rally in Pennsylvania.

Trump's odds of winning the election in recent days have edged higher on betting websites, although the outcome remains tight. 

Oddschecker.com had Trump at the equivalent of about a 56% chance of winning and Harris at about 44%, while a recent Wall Street Journal poll showed the two candidates tied across battleground states that could decide the election.

On the PredictIt platform, contracts for a Trump victory traded at 54 cents, with a potential $1 payout. Harris contracts were at 50 cents.

Trump's 57% stake in Trump Media ( DJT ) is now worth $3.6 billion.

Trump Media ( DJT ) soared 18% on Monday after reports that Democratic candidate Vice President Kamala Harris has agreed to be interviewed on Fox News on Wednesday. 

The stock has rebounded over 150% in recent weeks after closing at a record low on Sept. 24.

Trump Media ( DJT ) saw its value briefly balloon to nearly $10 billion following its stock market debut through a blank-check company.

Trump Media's ( DJT ) revenue is equivalent to two Starbucks coffee shops, and strategists say its current $6 billion stock market value is detached from its day-to-day business.