US stocks have surged as investors digest the Democrats’ victories in the midterm elections, lifted by hopes that Donald Trump’s turbulent policymaking would be restrained and shaking off initial fears about the impact on growth in the world’s largest economy.

The Dow Jones rose close to 3%, its best day in over a year, while the tech-heavy Nasdaq and the benchmark S&P 500 gained about 1.5% each when markets closed on Wednesday afternoon, turning around overnight falls in US stock futures after the news that the Democratic party won control of the Senate and the House of Representatives.

The price of oil dropped sharply as traders assessed the impact of the Democrats’ win on the war in Iran. Brent crude, the global oil benchmark, fell below $100 a barrel for the first time since early October.

In a social media post on Wednesday afternoon, Trump took credit for the jump. “Stock Market just hit another Record High,” he wrote. “Your 401(k)s are through the roof. Record Setting All!”

Related: After the US midterms, what will a lame duck Trump mean for the global economy?

However, the US dollar fell against the currencies of America’s major trading partners, hitting a one-month low on Wednesday while coming under pressure from falling bond yields. Investors moved into US treasuries, viewed as a haven from the political gridlock anticipated during the rest of Trump’s final term in office.

The dollar index, which measures it against a basket of six currencies, slid to its lowest level in a month, with the pound hitting its highest level since mid-September on the back of a fragile dollar, while the euro also made gains.

The dollar also slid against the yen and the Swiss franc, currencies that traders tend to turn to during times of uncertainty.

Meanwhile, the yield, or interest rate, on the benchmark 10-year US treasury bond has fallen 4.7 basis points to 4.918%. On two-year bonds it has dropped 3.7bps to 4.597%. Yields fall when bond prices rise.

Across the US, voters rejected Trump and the Republican agenda, with the Democrats securing Senate seats in traditional Republican strongholds such as Texas, Iowa, North Carolina and South Carolina.

Axel Rudolph, the chief technical analyst at the trading platform IG, said: “The scale of the losses will inevitably raise questions about Trump’s ability to push through his agenda over the next two years, and markets are already reacting. The dollar is under pressure as investors reassess the political outlook, while gold and silver are benefiting as safe haven plays.”

Futures trading initially indicated US stock markets would open sharply lower, with the Nasdaq expected to slide on fears over the prospects for AI companies. However, indicators later suggested Wall Street could open higher as Trump’s conciliatory tone and rises on European markets cheered investors.

European markets rose yesterday. London’s FTSE 100 was up 1.8%, Germany’s Dax rose by 2.2%, France’s Cac 40 was 2% higher and Italy’s FTSE MiB index rose by 2.2%.

Bank and clean energy stocks, which have borne the brunt of Trump’s policies, were among the top risers in Europe. Bank stocks rose by 2.8%, while Denmark’s Vestas Wind Systems jumped nearly 5% and Ørsted soared 7.4%.

“Some individual names are nursing significant losses today,” said Kathleen Brooks, the UK research director at XTB. “SpaceX is down 5% in the premarket, and Tesla is lower by more than 4%. Elon Musk is considered an anathema to most Democrats.”

Musk, the world’s richest person, pumped $446m (£331m) into the midterms, funding Republican-aligned political action committees and groups.

Brooks said investors were reacting to expectations that a Democrat-controlled Congress could mean greater scrutiny for AI companies, which could also cast doubt on a potential merger of Musk’s two companies.

Related: Trump’s wealth dented after Democrats trounce Republicans in midterms

The price of gold, a traditional haven asset, rose by 2.2%, soaring past $4,000 an ounce.

AI-related shares tumbled during Asian trading hours, on expectations that Democrats will want to bring in greater regulation of the sector.

Chris Turner, the global head of markets at ING, said: “Investors will be parsing what this all means. For example, Gina Hinojosa won the Texas governor’s race on a ticket of wanting an immediate moratorium on datacentre buildouts.”

He added: “Given AI’s role in powering the US economy, speculation over whether a new Democrat Congress would slow AI capital expenditure plans briefly hit markets.”

Jesper Koll, an expert director at the financial services company Monex Group, said: “The AI momentum has turned negative, with or without the Republicans having a majority. The starting point for financial markets into this election, particularly for the equity market, has been adverse on AI.”

Trump’s style of governing through executive orders has prompted some analysts to question whether the Democrats regaining control of Congress will have much change on US policymaking.

“There’s still a number of areas where Donald Trump can influence the markets – trade and tariffs, foreign policy and existing regulations,” said Tai Hui, a market strategist at JP Morgan Asset Management.