* Moscovici says confident Greece will conclude bailout program
* Urges Greece to keep up reforms, lenders to stick to debt relief
* Welcomes Greece's market return, after three years
* Tsipras says bond sale a step to exit the "bailout adventure" (Adds PM, Moscovici quotes)
ATHENS, July 25 (Reuters) - Europe's economics commissioner, Pierre Moscovici, said on Tuesday he was confident Greece was "turning a page" from economic crisis and would successfully conclude a bailout program which expires in Aug. 2018.
But Moscovici, who was visiting Athens, said the crisis-hit country was at a crucial juncture and urged Greece to keep up economic reforms.
"To legislate a reform is positive but to implement it is more significant," he told reporters.
He also said he was confident Greece could return to bond markets at "logical yields."
"Returning to the markets is an important first step," Moscovici told reporters.
Greece concluded a bailout review last month, paving the way for the disbursement of further funds after more reforms to its pension and tax systems.
On Tuesday, after a three-year hiatus, it launched a return to bond markets, widely seen as a test run for authorities before its third financial bailout from international lenders expires next year.
"It is also a signal to markets that Greece is showing results as far as its commitments are concerned and the reforms which have been decided and is back onto a path of sustainability," Moscovici said, speaking through an interpreter.
Greece has invited holders of its 4.75 percent outstanding bonds maturing in 2019 to tender them for cash, along with a plan to offer new five-year paper. Demand was strong early on Tuesday.
The country last ventured onto bond markets with two issues in 2014, a year before it lurched into crisis in a standoff with lenders which culminated in a third international bailout in mid 2015.
Prime Minister Alexis Tsipras told Moscovici that the bond sale was an important message and "the most significant step to finish this unpleasant adventure" of the bailout.
Moscovici told reporters it was crucial for Greece to keep up reform momentum, comparing it to riding a bicycle.
"Confidence in Greece is really coming back, but we need to continue the good work. We need to be on the bicycle, and to keep on pedaling."
"That's the case for Europe, as a whole. If you don't go that way, that bicycle falls."
He said the next bailout review would not be a "traditional" one and urged Greece's lenders to have a common and clear vision for the country and keep up promises on debt relief that were agreed in a meeting of euro zone finance ministers in June.
"The (debt relief) measures must be implemented at the end of the bailout program, but the decisions can be taken before that," Moscovici said. "We must continue to work hard toward completing the program." (Reporting By Renee Maltezou, writing by Michele Kambas Editing by Jeremy Gaunt)