Royal Mail shares rose 38% to 455p in their first day of conditional dealings on the London Stock Exchange.
The hugely oversubscribed sale was priced at 330p a share, valuing the 500-year-old firm at £3.3bn. At one point, the price hit 459.75p.
Private investors received 227 shares each. In all, more than 225 million shares were traded on Friday.
Business Secretary Vince Cable told Channel Four News he could have charged a higher price for Royal Mail shares.
Asked if he could have raised the sale price when he saw the level of demand for shares, Mr Cable said: "I could have done and I could have joined the speculators and spivs.
"I'm not interested in doing that," he said.
The shares are listed officially next Tuesday, but City institutions began conditional dealings on Friday.
Some 10 million shares were traded in the first 30 seconds when the market opened. Stockbroker Hargreaves Lansdown reported that its website was having "intermittent problems" due to the "unprecedented interest" in Royal Mail.
Tom McPhail, the firm's head of pensions research, said it was "extremely sorry for the delays", but was making "significant progress in clearing the backlog" and hoped to have all systems running normally again soon.
"We have experienced demand this morning which has gone off the scale," he said.
"We now have six times the normal number of staff working on our dealing lines. We know we are not the only broker affected by such problems this morning."
The price rise is likely to fuel debate over whether the sale of Royal Mail has been undervalued. Mr Cable has insisted that the taxpayer has not been short-changed by the privatisation.
But the general secretary of the Communication Workers Union, Billy Hayes, described the sell-off as "a tragedy" and predicted that it would make "not one scintilla of difference" to employees' intention to vote for strike action next Wednesday.
Mr Hayes told BBC Radio 4's Today programme: "This is a sham, really. The company has been undervalued.
"It's basically David Cameron rewarding his mates in the City. Vince Cable, one of the cleverest men in British politics, has made one of the stupidest decisions he is ever likely to make as a politician."
'Froth and speculation'
Mr Cable told the Today programme that the bulk of the shares had gone to "long-term stable investors" in the UK.
He said any volatility in the Royal Mail share price over the next week or so was of little consequence. "What matters is where the price eventually settles in three or six months' time".
Mr Cable said: "You get an enormous amount of froth and speculation in the aftermath of a big IPO [initial public offering] of this kind.
"The bulk of the shares have gone to long-term institutional investors, stable investors, some overseas investors, but mainly British pension funds and insurance companies who are there for the long term.
"The objective of the exercise, which fits in with what we want for the Royal Mail, is to make sure it has stable, long-term investors."
Voting in the strike ballot will close on 16 October. Under the current rules on industrial action, the earliest possible date for a strike is 23 October.
In the flotation prospectus, Royal Mail warned that labour unrest posed a potential risk for the share price.
Mr Cable said a strike was not in the interests of Royal Mail.
City analysts said the price rise was driven by big institutional investors' demand for the stock. Matt Basi, head of UK sales trading at CMC Markets, said investment funds were "queuing up to make big purchases".
Joe Rundle, head of trading at ETX Capital, called the surge in Royal Mail shares a "dazzling stock market debut".
But he said factors such as the threat of industrial action, a lack of adequate capital and unclear growth strategy could weigh down the stock price in the future.