* May urges EU to show flexibility on future relations

* Investors not convinced transition deal guaranteed

* Caps a poor week for sterling as Brexit risks dominate

* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv (Adds details, updates prices)

By Tommy Wilkes and Saikat Chatterjee

LONDON, March 2 (Reuters) - Sterling slipped against the euro and dollar on Friday after Prime Minister Theresa May urged the European Union to show more flexibility in talks on a future relationship but failed to convince investors a smooth Brexit transition deal is assured.

In a week in which sterling has fallen, the pound was initially unmoved by May’s comments but limped slightly lower against both the euro and dollar as the speech came to an end.

Against the euro, sterling fell as much as 0.5 percent to 89.470 after trading down 0.2 percent at 89.24 before May delivered her long-awaited speech.

Versus the dollar, sterling gave up its small gains to trade down 0.1 percent at $1.3763 at 1635 GMT.

The pound has suffered its worst week against the euro since October after comments by the EU’s chief Brexit negotiator, Michel Barnier, on Wednesday that a deal was far from guaranteed thrust political risk back onto the centre stage.

Amid a broad rebound in the dollar, sterling in February suffered its worst month versus the greenback since October 2016. On Friday, the dollar fell back against a basket of currencies but the pound failed to benefit.

Analysts said that while May’s speech suggested a transition deal - designed to buy Britain time to agree terms of exit from the EU – is one step closer, she did not say enough to convince investors an agreement would be hammered out by the end of March, when Britain has said a deal will be done.

“May’s comments signal one step closer to an agreement towards a transition arrangement and the weaker dollar is also keeping sterling supported. But we have to see more meaningful progress for sterling to break out of current ranges,” said Marc Chandler, global head of FX strategy at Brown Brothers Harriman.

With an Italian election and a vote on a German governing coalition both due on Sunday, investors have also been reluctant to take on any new large positions ahead of next.

Worries that Britain might not secure the post-Brexit transition period that it wants have overshadowed growing expectations that the Bank of England will hike rates in May thanks to better-than-expected economic performance and signs of inflationary pressures.

“May’s cogent and carefully laid out case will not necessarily drive negotiations forward so in the short term, paradoxically, it was read as negative by sterling buyers,” said Ken Odeluga, market analyst at City Index.

Some investors worry that delayed negotiations over a transition deal could make the BoE less likely to raise rates as early as May, as the market now largely expects. (Editing by Mark Heinrich)