ATHENS (Reuters) - Greece needs to stick to reforms to regain credibility and earn further debt relief, EU Economic Affairs Commissioner Pierre Moscovici said during a visit to Athens on Monday.

He said Athens and its euro zone partners financing its bailout need to reach an agreement with the International Monetary Fund on more debt relief by the end of this year. It is in the interest of all parties, Moscovici said, for the IMF to stay fully on board the program.

Saying that his visit was "a message of trust", the commissioner noted that Athens had made significant progress in reforming its economy and that the risk of leaving the euro common currency zone was no longer on the table.

But he urged Greece to avoid "complacency or backtracking" on agreed reforms, ahead of a second bailout review - which includes an unpopular loosening of labor laws - and is expected to begin in the autumn.

"It is time for normality, it is time for stability, it is time for implementation and it is time for investment," Moscovici said after meeting Prime Minister Alexis Tsipras.

"That doesn't mean that everything is done. We still have a way to go and there are discussions taking place and the need to complete some milestones for the first review and also to discuss the so-called second review."

Asked about Greece's desire to lower primary budget surplus targets beyond 2018, Moscovici said at a joint press conference with Finance Minister Euclid Tsakalotos: "Everything must be on the table ... but I would not suggest reopening this (issue)."

The IMF has also said that Greece's bailout target for a primary budget surplus of 3.5 percent of gross domestic product beyond 2018 is not realistic and has pushed for softer fiscal targets to take part in financing the third bailout.

Tsakalotos suggested that Athens may not submit its medium-term fiscal plan to parliament until there was an agreement with the country's lenders on its primary surplus targets.

"We'll discuss, we'll analyze those issues, we will see how the economy's funding needs will be affected and I believe that a solution will be found," he said.

(Reporting by Renee Maltezou; editing by Mark Heinrich)