Swiss ministers are in Washington for talks aimed at slashing US President Donald Trump's steep 39% tariffs on Switzerland's exports to the US – the highest rate in Europe.

Initial attempts by Swiss President Karin Keller Sutter to change Trump's mind fell on deaf ears. But a visit by business leaders appears to have changed his mind.

Swiss industry chiefs came to the Oval Office on 4 November bearing gifts, including a Rolex gold watch and a specially engraved gold bar from Swiss-based gold refining company MKS.

For months the Swiss have been trying to bring down the high US tariff rate which has already hit Switzerland hard.

Trump's response to the Swiss president's bid was that she was a nice woman, but she did not want to listen. But last week's private business initiative adopted a more unconventional approach.

Already this week Trump has said a deal is being worked on to bring the tariffs a little bit lower… I haven't set any number.

After their talks, Swiss industrialists said in a statement, our entire initiative was undertaken in the spirit of Swiss unity between the private and public sectors.

Some business figures, particularly those trading in luxury goods, gold, or commodities, already had contacts in Trump's circle. In September, Trump appeared at the US Open tennis final in the Rolex VIP box hosted by the Swiss watch company's chief executive Jean Frédéric Dufour.

The president, apparently guessing what was going on, even asked if Dufour would have been there if Trump had not slapped such steep tariffs on Switzerland.

Last week Dufour met Trump again, this time in the Oval Office, along with fellow business leaders including Johann Rupert from luxury goods maker Richemont and Marwan Shakarchi from MKS.

It is quite normal nowadays for any leader heading to the Oval Office to come bearing a gift.

Requests for confirmation of the gifts to the two Swiss companies involved brought a no comment from Rolex and MKS. But days after the meeting, Trump was pictured in the Oval Office with what looked very much like a Rolex Datejust desk clock, produced by the company as a collector's item, and worth tens of thousands of dollars.

A White House official confirmed the two items had been given to Trump. The US president receives thousands of gifts every year, and they then become US property, deposited with the National Archives and filed annually by the state department.

Swiss economy minister Guy Parmelin and chief trade negotiator Helene Budliger Artieda, who travelled to Washington on Wednesday, are more hopeful than they have been in months, amid suggestions that 39% tariff may be reduced to 15% - the same as Switzerland's neighbours in the EU.

In return, promises from the Swiss pharmaceutical giants to build more production plants in the US are already on the table. It is also reported that Swiss International Airlines, whose fleet is primarily Airbus, may pivot towards Boeing.

Fifa president and Swiss citizen Gianni Infantino, long a friend of Trump's, was reportedly urged by some Swiss parliamentarians to try to change the president's mind.

Whatever happens to the Swiss gifts, Trump's stance towards the Swiss appears to be softening, telling reporters he is working on something to help Switzerland.