Last week the oil giant, which produces more than a tenth of global crude supply, raised $25.6bn (£19.5bn).

Saudi Arabia's royal family is privatising assets as part of a plan to move the kingdom away from its reliance on oil.

The money raised from the sales will be used for non-energy investments.

Today's 10% rise, Riyadh's Tadawul stock exchange's daily limit, gives Aramco a market valuation of around $1.88tn.

That easily makes it the world's most valuable listed company but still less than the $2tn targeted by Crown Prince Mohammed bin Salman.

However it is still the biggest share sale to date, surpassing that of China's Alibaba, which raised $25bn in 2014 in New York.

Rocky road to market

It came after a testing journey for Aramco's public offering.

Saudi Arabia had to rely on domestic and regional investors to sell the 1.5% stake after lukewarm interest from abroad.

It initially sought to raise $100bn on two exchanges - with listings on the Saudi Stock Exchange, or Tadawul and an overseas market.

The plan was scaled back after foreign investors raised concerns about climate change, political risk, and a lack of corporate transparency.

International institutions were also unconvinced by the firm's valuation, prompting Aramco to pull marketing events in New York and London.

Instead, it focused its efforts on Saudi Arabian investors and wealthy Gulf Arab allies. Saudi banks also offered citizens cheap credit to buy the shares following a nationwide advertising campaign.

The share sale is at the heart of plans to modernise the Saudi economy and wean it off its dependence on oil.

The kingdom urgently needs tens of billions of dollars to fund megaprojects and develop new industries.

Analysis: Sameer Hashmi, BBC Middle East Business Correspondent

It was widely expected that Saudi Aramco shares would get off to a blistering start - thanks to the strong backing of local affluent investors and Saudi institutions - who were asked to buy shares at the start of trading.

Friendly gulf neighbours like the United Arab Emirates and Kuwait have also helped bolster the share sale by pumping in billions of dollars. The Kingdom's energy minister is confident that the company's valuation would breach the $2 trillion mark in the coming days. Analysts expect the share price to remain firm in the near future but also say that the real test would be to sustain the momentum in the long run.

The IPO is at the heart of Saudi Arabia's ambitious plans to diversify its economy away from oil. The Kingdom's crown prince - Muhammed bin Salman (MbS), who is spearheading the economic strategy - wants to use the IPO proceeds to part-fund some key initiatives announced under a programme called 'Vision 2030' that aims to modernise Saudi Arabia's economy by investing in new industries and multi-billion dollar projects.