* Euro dips but remains above 2-year lows
* Yen rebounds with Trump in Tokyo
* Sterling still stuck below $1.27 on Brexit worries
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
LONDON, May 28 (Reuters) - The euro dipped on Tuesday as investors nervous about trade tensions bought into the safe-haven dollar and fretted that political risks in Europe remain high, even though pro-Europe parties won a majority of European parliamentary seats.
Remarks by two euro zone officials that the European Commission was likely to fine Italy on June 5, because its rising debt and structural deficits break European Union rules, also weighed on the single currency.
Pro-Europe parties kept a majority of seats in last week's European parliamentary elections. Support grew for eurosceptic and right-wing parties, but not as much as investors had feared.
European leaders now meet in Brussels to fill in a number of top EU posts, from the head of the European Commission to the European Central Bank.
"I wouldn't be surprised if the market is still digesting the European election results. Things still don't look very promising as the focus moves to who gets which job in Europe," said Commerzbank currencies analyst Thu Lan Nguyen.
Currency markets remain in tight ranges without new catalysts and amid uncertainty over how trade tensions between the United States and China are affecting the world's major economies.
The euro slipped 0.1% to $1.1179. The single currency did gain initially after the EU election results, but not for long.
The dollar rose 0.2% against a basket of peers, its index touching 97.791. It remains off a two-year high of 98.371 hit on Thursday.
The yen was in a holding pattern, rising 0.2% to 109.35 yen . U.S. President Donald Trump, who is visiting Japan, is expected to put pressure on Tokyo to reduce the nation's large trade surplus with the United States. The Japanese currency
Trump said on Monday he expected the two countries to be "announcing some things, probably in August, that will be very good for both countries" on trade.
"While it's positive that there will be time for solving the U.S.-Japan trade issue, that doesn't mean the problem has been has been resolved," said Kumiko Ishikawa, senior analyst at Sony Financial Holdings. "(But) it's providing some relief."
Ishikawa said the still-unresolved trade disputes between the United States and China made it hard for investors to take on risk.
Elsewhere, the Australian dollar gained to $0.6923, about 0.75% above Thursday's four-month low.
The Swedish crown rallied 0.3% to 10.689 crowns per euro despite a weaker than expected consumer confidence reading.
Sterling slipped 0.1% to $1.2671 as candidates to succeed British Prime Minister Theresa May laid out some of their Brexit plans. (Additional reporting by Daniel Leussink in Tokyo, editing by Larry King)