* Dollar inches higher with U.S. yields as oil gains for third day
* Eyes on Draghi speech later in day
* Sterling higher as May seals needed support for government
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Patrick Graham
LONDON, June 26 (Reuters) - Financial investors' lack of faith in another rise in U.S. interest rates this year kept the dollar near one-week lows on Monday at the start of a week packed with speeches from Federal Reserve and other senior central bank officials.
A third day running of higher oil prices had investors buying a number of major currencies including the dollar against the yen in morning trade in Europe in the hope that crude will hold inflation down less.
Sterling recovered more ground as Prime Minister Theresa May sealed the support she needs to win a vote this week on her minority government's programme, helped by a shift by some at the Bank of England towards raising interest rates.
But markets so far are loathe to buy the Fed's own line that it will raise U.S. rates once more before the end of 2017 and another three times next year. Even with a blip higher in morning trade, 5- and 10-year Treasury yields are up to 45 basis points below highs hit in March.
The dollar traded 0.15 percent stronger at $1.1176 per euro and a third of a percent higher at 111.72 yen by 1115 GMT.
"Market expectations are for a lot less (on rates) than what the Fed say they are going to deliver ... so oil's forming a base this morning has supported Treasury yields and the dollar," said Sam Lynton-Brown, a strategist with BNP Paribas in London.
"(But) for any rise in U.S. yields and the dollar to be sustained we are likely to have to see a more convincing pickup in U.S. economic data."
Fed chair Janet Yellen makes a hotly awaited speech in Europe on Tuesday but most analysts were skeptical of the chances of her driving the greenback sharply higher.
"The market continues to call the Fed's bluff on its intentions to change rates. I don't think anything Yellen can say this week will change that," said Stephen Gallo, head of European FX strategy with Bank of Montreal.
"We were saying buy dips in cable and euro (against the dollar) last week. We still look for the same this week."
Yellen is preceded by European Central Bank chief Mario Draghi on Monday, watched for signs he is ready to let the ECB move more forcibly towards a reduction in emergency stimulus for the economy this year that should support the euro.
Some say steadier oil prices would help Draghi sign up behind the move towards normalising policy being advocated by Germany's Bundesbank, but so far he has been reticent, worried that, not for the first time since 2008, the euro zone's recent pickup may prove less durable than hoped.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Shinichi Saoshiro in TOKYO; Editing by Jeremy Gaunt