LONDON (Reuters) -The dollar rallied on Tuesday as investors took comfort from U.S. President Donald Trump's decision to delay higher tariffs on the European Union, while the yen came under pressure from a sharp fall in Japan's long-dated bond yields.

With U.S. and UK markets closed for a public holiday on Monday, analysts said some traders were still catching up with Sunday's news that Trump had delayed tariffs on the EU.

While that news boosted the euro on Monday it was also viewed as positive for the dollar, which was broadly firm on Tuesday, with the dollar index last up around 0.4%.

"I would guess it is because Trump retreated over the weekend. Yesterday markets were closed so there was only a small move, now with the UK being back it's a recovery of the move we saw on Friday," said Commerzbank FX analyst Michael Pfister.

Dollar strength was most visible versus the yen.

The dollar was up 0.75% at 143.91 yen as long-dated Japanese government bond yields fell sharply after a Reuters report that the country's Ministry of Finance would consider trimming issuance of super-long bonds in the wake of recent sharp rises in yields for the notes.

"It's a big move so obviously it's dragging down the currency," said Francesco Pesole, FX strategist at ING on the move down in Japanese bond yields.

"The yen is still probably the G10 currency - outside of the dollar - that has more domestic drivers."

Japanese Finance Minister Katsunobu Kato said on Tuesday the government was closely watching the debt market, while Bank of Japan Governor Kazuo Ueda said the central bank must be vigilant on rising consumer prices in Japan, signalling its readiness to keep hiking rates.

Bond yields, particularly on the long end, have surged globally on mounting concerns over growing fiscal deficits in advanced economies, led by the U.S. and Japan.

Attention turned to debate in the U.S. Senate on Trump's tax-cut bill that is expected to add to the debt pile in the world's largest economy. Markets have been sensitive to Trump's proposal, particularly after Moody's downgrade of the U.S. sovereign credit rating on May 16.

The U.S. House of Representatives last week passed a version of Trump's tax-cut bill that is calculated to add about $3.8 trillion to the federal government's $36.2 trillion in debt over the next decade, according to the Congressional Budget Office.

Trump said on Sunday that the bill was likely to see "significant" changes as it is debated in the Senate.

Investor confidence in U.S. assets has been undermined in recent months in the wake of Trump's erratic tariff policies.

In the latest example, Trump backed down from threatened 50% duties on EU shipments from June 1, sending the euro rallying to a one-month high.

The euro was last down 0.3% against a broadly firm dollar at $1.1346, while sterling slipped almost 0.2% to $1.3542 and the dollar gained 0.6% against the Swiss franc to 0.8258.