SINGAPORE (Reuters) -Shares of European drugmakers slipped on Friday after U.S. President Donald Trump sent letters to major pharmaceutical firms to cut drug prices in the United States, months after signing a sweeping executive order aimed at lowering prices.

The letters were the latest setback for a sector still grappling with the prospect of tariffs outlined in the U.S.-EU trade deal that could cost the pharmaceutical industry between $13 billion and $19 billion.

Trump called on 17 drugmakers to provide so-called most-favoured-nation prices to every patient enrolled in the government Medicaid health programme for low-income people, and to guarantee such pricing for new drugs.

Shares of European drugmakers Sanofi, AstraZeneca, GSK, Merck KGaA and Novo Nordisk slipped between around 1% and 4% in early trading on Friday. Novo's 4% fall extends a selloff this week that started on Tuesday with a 28% plunge, wiping out $70 billion of its market value after the maker of weight-loss drug Wegovy issued a profit warning and named a new CEO.

The companies were all sent letters by Trump, who gave them until September 29 to respond with binding commitments to those terms. U.S. drugmakers including Pfizer, Johnson & Johnson, Eli Lilly and Merck were also sent the letters.

The European healthcare index was down 1.4% by 0731 GMT, its lowest since April.

"Trump's directive to the pharma companies will put them on the defensive and adds yet another layer of uncertainty for the sector which could also face import tariffs in time to come," said Vasu Menon, managing director of investment strategy at OCBC.

"While Trump has set a deadline for these companies to comply, it remains to be seen if this is hard coded or if he will roll back some of his threats if these companies make an effort to engage him and soften his stance."

Analysts, lobbyists and drug pricing experts though said it seemed unlikely that the pharmaceutical companies would comply with Trump's demand to lower U.S. prices.

The companies including Pfizer, AbbVie, and German Merck KGaA's U.S. division, EMD Serono, said they were open to working with the Trump administration.

Trump's executive order in May directed drugmakers to lower medicine prices to align with what other countries pay, leading to some shift in how drugmakers look to sell their medicines.

Swiss drugmaker Roche said last week it was considering selling its prescription medicines in the United States directly to consumers to lower costs for patients as part of talks with the U.S. government.